If no restriction is listed (and I can confirm that none is), no restriction exists. It’s related to psionics because the only classes that have it in-class are psionic classes, but others can use it just fine. As you say, there’s no reason it should be restricted, and lo and behold, it’s not.
Tier 0 isn’t really a thing—JaronK’s tier list enjoys a lot of consensus, but only includes tiers 1 through 6. That list mentions the truenamer as being basically broken and not really fitting into the tiers, which is sometimes referred to as tier 7 (or simply “truenamer tier”), but beyond that there are just the six.
Furthermore, for the most part, the tiers very much want to treat classes by their full range of potential—from the naïve no-op build to a full to-the-hilt optimized build. The idea is that for a given amount of optimization, higher-tier classes are more versatile and/or powerful, and lower-tier classes are less versatile and/or powerful. The main point here is that generally speaking, class variants and options aren’t considered separately in the tier list—they just represent more or less optimization. There are a few exceptions—dungeoncrasher, for example—but for classes that are already tier 1, an option that makes them more powerful isn’t really considered relevant.
That hasn’t stopped people talking about the idea of things that are even stronger than what we think of as tier 1. Psionic artificer is notable for having dramatically more versatility than a regular artificer—which is already an incredibly versatile class, even by the standards of tier-1 classes. That’s notable. Sometimes the psionic artificer is therefore called as tier 0, or as the link offer suggests, “If there is a Tier Zero, Psi Arty deserves it.”
Spell-to-power erudite is also a frequent candidate for tier-0 status. Again, we’re talking about a character that has dramatically more spell access than a cleric or wizard, plus most of the power access of a psion. This thread has several people calling it tier 0, for example.
But ultimately, none of these things have even remotely the consensus that the main tier list has. Tier 0 isn’t really a codified thing, it’s just an occasional topic of conversation. Psionic artificer and spell-to-power erudite are some of the most common choices for those conversations. I don’t think you’ll find many people who will say “no, that isn’t tier 0!” though.
Best Answer
This is based on the 3.5 version of the wilder; in the past I’ve looked at the Pathfinder improvements and determined them to be too little, but I don’t remember the details at the moment, so Pathfinder-specific commentary will have to wait until I do some double-checking and refreshing.
In theory, the ability to break past the usual Manifester Level limit on augmenting powers. In practice....
Using the aforementioned advantage requires taking an enormous risk, both short-term and medium-term. You lose your next turn, which can be devastating and dangerous, and you lose a lot of power points. Psychic enervation is incredibly dangerous.
Compare this to Overchannel, a feat available to any manifester. Yes, Overchannel always deals damage to you, and scales slower than Wild Surge. That said, it is predictable and relatively low-risk: you know exactly what you’re putting on the line with Overchannel, and it’s something you can handle. Wild Surge gives you a chance of getting off scott-free, but it also gives you a chance of being put in a massively dangerous position and losing critical resources. Most of the time, Overchannel’s the better option. That is, the unique, special ability of the wilder class is often worse than a feat available to anyone.
And the cost for this class feature that’s often worse than a feat is massively fewer powers known and a far more limited selection of powers, compared to the psion. The psion’s Intelligence focus also makes it rather more suited to being social, given that it can actually afford the skill points.
Not really; Wild Surge is a bit larger than Overchannel but narratively it’s basically the same concept. You could easily make the same concept as a wilder by using a psion who uses Overchannel.
Basically impossible; you can just not use Wild Surge, of course, and a lot of wilders end up doing that most of the time, but then you get nothing for the massively restricted powers known and power list. And adding additional powers known is extremely hard.