Fanaelialae
Legend
I don't believe there should be an automatic success on a 20 or failure on a 1, because this negates several class abilities, especially for contested rolls. I had an 11th level rogue in my game who's minimum roll for stealth was 23 (all rolls less than 10 became a 10), so I'd check the monster's maximum Perception. If the roll couldn't get to 23, I wouldn't even bother to make any rolls. If it could, I'd check to see if they even got to the minimum, and only then would I bother the player to roll. It actually saved time, and the player felt vindicated that his specialization (which came at the cost of other options) was useful.
Additionally, this takes away from the rule of the DM determining the outcome of an action and only using dice when the outcome is uncertain. If a 20 is always a success, or 1 a failure, then there is ALWAYS uncertainty, allowing players to do some really silly things (like jumping to the moon, or tripping over their own feet while walking) 5% of the time.
You can have auto fail on a 1 and auto success on a 20 without the things you suggest. The DM just needs a modicum of common sense.
Want to jump over the moon? Sorry, I don't care what your bonus is, under normal circumstances not gonna happen.
Want to jump over a pebble? Okay, barring something really weird, you just succeed (no roll).
However, I don't like the idea that your rogue could sneak through a court yard filled with minimal cover patrolled by a hundred (or a thousand) guards proficient in stealth but without a wisdom bonus (+2 perception) without any possible chance of failure. Sorry, not going to happen at my table. The rogue will have an excellent chance for success, but on a natural 1 he will fail because he is attempting something that would be nearly impossible for a lesser character. I think 5% chance to fail is quite reasonable in that scenario.
Conversely, if Grog the barbarian is trying to kick down an ordinary door, it's not a question of whether or not he will succeed, just whether he can do it in a single kick (potential surprise) or not (enemy will have weapons drawn). If there are no creatures in the vicinity, I wouldn't even have him roll, since success is a foregone conclusion.