When They're Worth the Cost
For characters like animal instinct barbarians or monks with better unarmed attacks, there may not be much use in taking these abilities. But for various characters like the goblin wizard or even just a regular fighter looking for a guaranteed backup option, the benefits may outweigh the typically low costs.
Benefits of Ancestral Unarmed Attack
You've mentioned quite a few reasons it might be worthwhile to get an unarmed attack beyond the standard 'fist', including as a backup if weapons are taken away and freeing up whatever hands a weapon would use.
Having an additional free hand opens up quite a few Athletics actions like Trip and Grapple that render foes flat-footed to your entire party, as well as allowing the Grab an Edge reaction without needing to let go of a precious weapon if someone knocks you off a cliff.
Additionally as ESCE mentioned below, there's value in having multiple damage types available in case of enemies with resistances, immunities, weaknesses, or other circumstances. Dealing 1d6+10 on a bite against piercing weakness would potentially be better than 2d8 slashing with a striking weapon, even factoring the +1 accuracy.
And while a spiked gauntlet would be pretty good as an alternative for one of these cases, it deals less damage than many of these ancestral unarmed attacks and isn't finesse for characters that lack Strength.
Additionally, not all ancestral unarmed attacks deal physical damage—there's also options like an automaton's energy beam dealing fire.
Character-Specific Benefits
Virtually all characters are at least trained in unarmed attacks, while many are not trained in martial weapons like shortswords or warhammers. A wizard with a surprising d6 bite attack might come in handy compared to drawing out a dagger (requiring an open hand) and dealing less damage. Or an alchemist firing a laser out of their eye might make a good ranged option when there aren't any bombs left.
Not to mention that with some options there are more ancestry feats associated with the unarmed attack. Like the goblin's bite in the reaction Ankle Bite and Hungry Goblin, allowing more specialization and benefits using these unarmed attacks as you level up. Whether any ancestral unarmed attack has similar synergistic options will depend on the specific case, a goblin building around that bite attack by taking those ancestry feats seems like an interesting character with advantages over other attack options.
And with versatile heritages like dhampirs, beastkin, and tieflings, these options are available to virtually any character regardless of ancestry, with varying levels of additional support through higher level ancestry feats.
Flavor
There's also the simple benefit to being something like a sabre-tooth catfolk or an automaton shooting lasers out of their eye. Having an ancestral unarmed attack might be a core piece of character identity that a player will try to optimize around, rather than considering it as part of optimization.
Costs of Ancestral Unarmed Attack
In most cases, a 1st-level ancestry feat or heritage. Some ancestries like humans have great 1st-level ancestry feats (Natural Ambition comes to mind), but others have more niche uses/fewer options that appeal to every sort of character.
For one of your examples, a Catfolk adventurer may not be interested in being a bit luckier on Reflex saves, dancing, knowing the ancestral lore of their people, or fighting with their ancestral weapons. In this case, the opportunity cost of one 1st-level ancestry feat would be low, and the benefits are more likely to outweigh it.
And at the low levels these abilities are available, upgrading the unarmed attack isn't required. Retraining out of these feats when they become less useful relative to your magical weapon(s) is an option as that becomes a problem.
There's also the 3rd-level general feat Ancestral Paragon that allows characters to gain an additional 1st-level ancestry feat, granting even more opportunities to take these abilities in situations where options are limited.
Are They Worth It?
Probably not for many characters, particularly if an alternate option is more attractive, they have stronger attacks from a class, or they don't worry about the problems an ancestral unarmed attack would cover (knowing your GM isn't 'sadistic' certainly helps).
That said, characters with weaker alternative options from their ancestry/heritage/class, or who are looking for a particular attack like a laser eye could find these options good enough to take. And characters specializing in these attacks with synergistic, higher-level ancestry feats might be worthwhile on their own merit.
Yes, you can
From rune rules we get the distinction between fundamental runes and property runes
Runes must be physically engraved on items through a special process to convey their effects. They take two forms: fundamental runes and property runes. Fundamental runes offer the most basic and essential benefits: a weapon potency rune adds a bonus to a weapon's attack rolls, and the striking rune adds extra weapon damage dice. An armor potency rune increases the armor's item bonus to AC, and the resilient rune grants a bonus to the wearer's saving throws. Property runes, by contrast, grant more varied effects—typically powers that are constant while the armor is worn or that take effect each time the weapon is used, such as a rune that grants energy resistance or one that adds fire damage to a weapon's attacks.
Here we get that the limitation to # of runes is limited to property runes, not fundamental runes
The number of property runes a weapon or armor can have is equal to the value of its potency rune. A +1 weapon can have one property rune, but it could hold another if the +1 weapon potency rune were upgraded to a +2 weapon potency rune. Since the striking and resilient runes are fundamental runes, they don't count against this limit.
Finally, we get the magic word "typically" here, which is definitely not "always"
An item with runes is typically referred to by the value of its potency rune, followed by any other fundamental runes, then the names of any property runes, and ends with the name of the base item. For example, you might have a +1 longsword or +2 greater resilient fire-resistant chain mail.
Looking at the fundamental runes rules we get that magical word "typically" again:
An item can have only one fundamental rune of each type, though etching a stronger rune can upgrade an existing rune to the more powerful version (as described in each rune’s entry). As you level up, you typically alternate between increasing an item’s potency rune and its striking or resilient rune when you can afford to.
While the cost for upgrade cost shows only examples starting at +1, it once more expressly calls out typically, and even gives an example (though not the "no potency" example) of one where you might skip up the striking path:
This also indicates the typical progression for an adventurer to follow when upgrading their armor and weapons. The tables here don’t include progressions that aren’t as likely to come up, like turning a +1 weapon directly into a +1 greater striking weapon.
Nowhere else do the rules runes list any limitations on fundamental runes. So you can have all the striking you want without any potency, though you wouldn't be able to add property runes until you had potency runes to allow for it.
To address the additional question, not only would the exact same logic apply to resilient runes, it would be far more likely to find broad applicability there. Not every character cares so much about armor class, whereas everyone cares about saving throws, so much so that previous editions came up with ways of letting you stack +resistance to saving throws on top of other items without penalty.
Best Answer
Handwraps of Mighty Blows Can't Modify the Attacks
Normally none of the statistics granted by a battle form polymorph spell like animal form can be adjusted outside of circumstance/status modifiers. However, many if not all such spells include an exception like this:
So while you can't improve the attack granted like the ape form's 2d6 bludgeoning fist, you could improve your own unarmed attack bonus to use in place of the +9 or whatever modifier is given by the spell. If this is your only reason for getting handwraps it might be worthwhile to leave off the striking runes.