As far as I know there isn't one in UNIB yet. There is an activation of some sort, but I don't remember what it does.
Practically every other type of entertainment that can be taken to a competitive level, from actual sports to Chess to card games, don't have anything akin to this. So, why is it that fighting games "must" have this, I wonder...?
That's debatable for certain card games that I will not mention.
With regards to "comeback mechanics," I think its the developers trying to incorporate strong options. However, the problem comes when the mechanic is too strong or one-dimensional. One good way to see this is to compare Heat Activation and XFactor.
XFactor (forgive me if I get any of this wrong, I don't play MvC3):
Has its own bar
Fairly large damage boost, varies based on XFactor "Level"
Speed boost, varies based on XFactor "Level"
Can be used to cancel just about anything
HP recovery, varies based on XFactor "Level"
Heat/Max mode:
Uses Magic circuit just like EXs do
HP recovery, stops when blocking or hit, speed depends on moon and version of heat mode
Can be used to cancel certain moves (full moon only)
Slight damage and defense boost (crescent moon only)
Can be used to get out of combos (bursting)
Bursting happens automatically (Half Moon only)
Can be used as a pseudo-reversal (activation)
The first thing I'd like to point out is that Heat Activation is primarily defensive. It has three offensive applications, one for each moon: IH canceling, auto-burst, and damage/defense boost. But other than that it is defensive: getting out of combos, reversal, HP Recovery.
It also has a lot of utility on usage. Since it uses the same meter as the EX moves we are forced to choose between using the activation and using the EX moves (or a combination of both). Full can use IH canceling for just about anything.
Comparing that to XFactor, XFactor is extremely one-dimensional. It's primary usage is offense, as a damage booster to kill, as a cancel to continue a combo for a kill, or as a speed booster to get an attack in (to kill). The healing is just an extra bonus, people probably would complain about it just as much if there was no healing attached.
Also when comparing the two, it should be noted that the bonuses that they share are Stronger in XFactor. The damage boost is higher and the healing is faster.
Enough of that, let's get back to discussing UNIB.