What if they had implemented psionics, as per 2nd edition AD&D psionics rules? Would the game be better or worse?

I'm thinking it would work best along these lines:
No wild talents (keep things simple)
Psionicist available as a PC class
Most enemies would not have psionics. Exceptions would be creatures that have been traditionally given psionic treatment in the P&P game (such as BG2's mind flayers)

What would you think of this addition to the game? Would it make the game more enjoyable? Or would it ruin the game? (Remember, AD&D psionics isn't what you would call balanced before 3rd edition.) Or would you simply ignore the psionicist class and have the game feel about the same?

I don't see the point. The rules as created for BG are simplified and custom rules, not P&P rules. Most psionics schools and abilities already have arcane equivalents (a kineticist is pretty much covered by an evoker etc.) It might have been interesting to see how they approached it in a "what if" scenario, but keeping things simple is one of the trademarks of BG; would the game have 'felt' the same? Who knows.

Would it affect our ability to polymorph past walls, through a black hole (bring a towel) and past the final boss of the game?

It depends on what sort of powers are implemented, and on how well they are implemented. (A poorly implemented power could lead to some silly glitches.) If a polymorph power (or even something that changes the user's size) is implemented, it could allow polymorph teleportation, possibly at a low level in BG1, making the game easier to break. (Of course, maybe a power like Dimension Door might be more interesting in BG1, as it would allow the Dimension Door glitch to be used.)

There are no black holes in the series (or at least I don't think there are).

Going past the final boss would not beat the game, unless some way to trigger a credits warp is found.

By Bhaal's left leg, I really hope you're trying to play along here...

When did you become "human"? What has happened with dog on your avatar?

In all seriousness, I think the parts of the game where you fight mind flayers would definitely be different. The Complete Psionics Handbook gives them new powers such as detonate, control body, and dominate. In other words, as if they weren't bad enough already, they can now turn your allies against you. (Detonate could be a pain if they implemented the destruction of items when it triggers.)

Of course, the higher tiers of mind flayers would have even more powerful psionics, but because such powers are not level gated, it isn't as bad as fighting more powerful casters would be.

On the other hand, imagine the implications of psionic combat when you encounter mind flayers with a psionicist in your party. All of the sudden, mind flayer battles just got a lot more complicated.

(By the way, I believe there is a consumable item that says it makes the user immune to psionics. Does that include non-telepathy powers or those that are benificial to the target?)

Can't you tell? That *is* the dog, who's evolving even still...