A Blinded, Blindsight-possessing caster can still cast its sight-dependant spells
The Blinded condition is defined as;
A blinded creature can't see and automatically fails any ability check that requires sight.
attack rolls against the creature have advantage and the creature's attacks have disadvantage
while blindsight is written as;
A creature with blindsight can perceive its surroundings without relying on sight, within a specific radius
A creature with blindsight does not require or rely on sight within the specified radius so the first aspect of the blinded condition is nullified within the region of blindsight. the second aspect however is not directly countered.
RAW a creature with blindsight can still do anything that requires sight within that range including casting spells, but would have disadvantage on attack rolls due to the blinded condition.
creatures that have no eyes such as oozes are already immune to the blinded condition so there shouldn't be any issues with the inherent logic with them. but a creature with blindsight that is blinded (such as the aforementioned dragon) would still be worse off than one that is not blinded.
As written, yes, hunger of Hadar is “seriously overpowered.”
What is written for hunger of Hadar is that “creatures fully within the area are blinded.” Even as an English phrase, “are blinded” is an event, something that has happened to a creature; absent any context, we generally assume that it’s permanent. Consider how common the phrase “temporarily blinded” is, just avoid that assumption.
Now, in context, we have the actual game rules about conditions. Those say
A condition lasts either until it is countered (the prone condition is countered by standing up, for example) or for a duration specified by the effect that imposed the condition.
Here we have “A condition lasts until,” that is, until one of the following events take place, the condition lasts, period. Then we have two events listed after “until,” either of which is sufficient to stop the condition from continuing to last:
the condition is “countered,” or
a “duration specified by the effect that imposed the condition” runs out.
But hunger of Hadar doesn’t build in any special circumstances that counter the blindness, so only generic effects that can remove blindness—e.g. lesser restoration—are going to apply. Even dispel magic and the like are somewhat dubious: those can remove hunger of Hadar’s shadows and stop it from blinding anyone else, but it’s not clear that the blindness condition itself is a spell effect that can be dispelled.
And hunger of Hadar also does not specify any duration for the blindness condition. It just says “creatures fully within the area are blinded,” nothing more. Nothing about that blindness ending at any point.
That leaves us with hunger of Hadar permanently blinding every creature that has ever been “fully within the area.” And yes, permanent blindness applied to every creature that ever found itself within hunger of Hadar is seriously overpowered, and that is what is written, technically, in the books.
But we can give more context here—our familiarity and expectations of the game. One of those is that things shouldn’t be “seriously overpowered,” as we just determined hunger of Hadar is, as written. It seems likely that the authors and editors of hunger of Hadar forgot that conditions basically default to permanent, or missed its implications, and considered their wording as “obviously” meaning the condition only applies as long as creatures are within. It seems they almost-certainly meant that the creatures are blinded for a duration equal to however long they stay fully within the area of hunger of Hadar, or that (partially) leaving the area of hunger of Hadar counters the blindness. That would make for a reasonable spell. That is how the majority of people, it seems, assume the spell works, because they assume the spell isn’t “seriously overpowered” and read it within that context without checking the actual technical definitions.
But the game’s authors, really, should have double-checked. They should have included that duration, or that countering event, in the rules text. It wouldn’t have taken much, just a clause like “until they leave the area” in the description. But they didn’t include that. They made a mistake, it seems.
Mistakes happen; there are a lot of interactions in a game system, and ultimately they’re all interpreted by a person who may inject their own sensibilities into things—making it very difficult to recognize that those sensibilities had to be injected in the first place. Ultimately, being careful with that is part of what we pay a game developer for; a large chunk of the value they purport to offer to customers is their expertise and care that allows them to provide more consistent and balanced material than you could do on your own. They didn’t here; that failure counts, even if it is easily corrected. It is fair, I think, to “hold it against them,” to some extent—and if this kind of thing happens a lot, for that to damage your perception of the quality of their product.
But in the end, there will always be mistakes. That’s unavoidable. If you find that 5e is just rife with issues like these, that’s a knock against it. If it happens only rarely, though, then it’s a sign that it’s well-made—don’t over-emphasize any single mistake either. I leave the adjudication on the relative frequency here to others. Hopefully, Wizards of the Coast will explicitly mention at some point that hunger of Hadar only blinds things for as long as they’re within. But in the meantime, their mistake is no reason for you to allow it to mess with your game. You easily can, and should, correct for it yourself.
Best Answer
Tremorsense does not provide "sight"
To begin the description of tremorsense does not imply that it allows it to replace sight (DMG, 9):
This description is specific in what it allows tremorsense to detect: "the origin of vibrations". In practical terms it is easy to imagine a monster using vibrations to detect a creature's location. It is harder to imagine vibrations equalling sight for the purpose of determining where an archer is aiming or other minute details.
There is also nothing indicating that tremorsense allows a monster to pinpoint non-vibrating objects. It can hardly qualify as "seeing" if the creature cannot detect a door or a pillar in its way.
The description of tremorsense can be compared to the description of blindsight which offers more generic perception (DMG, 8):
The understanding that tremorsense, unlike blindsight, cannot replace regular vision is further supported in the passage describing Vision and Light1. This passage explicitly mentions blindsight, darkvision, and truesight as exceptions to the regular rules for sight. It makes no mention, however, of tremorsense being an exception to the rules of sight.
If tremorsense were intended to provide sight it would say so and would be more aptly names tremorsight, or tremorvision in line with blindsight, truesight, and darkvision.
Tremorsense is not used as a substitute for sight in published monsters
Unlike with blindsight there are no monsters that rely exclusively on tremorsense for perceiving their surroundings. This makes sense in that every monster with tremorsense in the Monster Manual, except for Galeb Duhr, also has a burrowing speed. The description of tremorsense also notes that it is generally possessed by burrowing creatures. Tremorsense is then used to identify when other creatures are nearby underground. For this purpose the location of the creature is sufficient because if the monster were in a situation where sight were relevant it would be near enough to rely on darkvison or blindsight.
Excluding the Borborygmos, Mantrap, Sacred Stone Monk, and Stonemelder all published monsters with tremorsense at this time also have blindsight or darkvision with which to see. The Borborygmos has the feature Poor Depth Perception which causes disadvantage on targets more than 30ft away. If its 60ft tremorsense could replace sight then one would imagine Poor Depth Perception would only apply outside of a 60ft radius rather than outside a 30ft radius.
Of monsters with tremorsense only the Core Spawn Crawler lacks regular vision. The Core Spawn Crawler provides additional evidence that tremorsense does not allow sight because its blindsight reads:
If the crawler's 60ft tremorsense could allow it to see then it would be inaccurate to say that it was blind beyond 30ft. The "blind beyond this radius" note would be better placed after tremorsense if tremorsense could replace sight.
How is tremorsense treated conventionally?
I cannot speak to the "average" dnd gameplay but one of the strengths of DnD-5e is its simplicity and universality. If, in fact, many players use a different understanding of tremorsense then the prevailing norm could be more important than a strict RAW interpretation. Ryan C. Thompson provides a reason in their answer to a related question to allow tremorsense to replace sight:
Concerns of simplicity are important and the convention of a table trump RAW. If a DM wants tremorsense to replicate sight that is their purview regardless of whether it derives from a different interpretation of the text or from a desire for simplicity.
1: Credit to Mark Wells for this argument
2: Tremorsense is effectively a substitute for vision for targets that it can detect.