I think following the P&P papers is best, so natural 20/1 being auto miss/hit in combat is fine, while it shouldn't be used for skill checks - at least not, for skill checks that are not performed under acute pressure.
Generally, I wouldn't agree that a hit chance of 0% or 100% is a bad thing in general - XCOM has 100% hit chances and combat is fine - better than almost any RPG with turn-based combat in my opinion.
Of course, you can construe a scenario where a hit chance of 0% puts you in an impossible situation, but is that really different than being an almost dead melee fighter who isn't close enough to attack the wizard who is going to cast magic missile next? Or when you start the round with a damage-over-time effect (like a burn), are almost dead and can't possibly do enough damage in one turn to end the fight? Impossible situations already exist in combat. The same scenario you describe has slight variations which are actually interesting: imagine you only win the fight because you counterspelled the boss boss. Or you manage to survive for 2 rounds and dispel the buff in the first round only to kill the boss in the 2nd. Or buff yourself, or use an ability that increases your chance to hit for one attack.
But again, this is a D&D game, the rules are fine, they should use them here.
