There is a problem with skills - in some cases they can be retried for free. In this case, you can assume that people would finally roll 20. With your solution, it means that can accomplish ANYTHING. Think about epic skill usages from Epic Handbook from 3rd edition. Pass through wall of force? DC 120. What is the problem, I will succeed on 20. Even if you don't allow rerolls for such skills, still one in 20 peasants will teleport through it.
Climb on the smooth ceiling ? Why not. Run over water? One in 20 will succeed. Swim up waterfall? Done.
Of course, there are no such DCs yet in 4th edition. But you are opening up possibility of doing the impossible by just trying hard enough.
In combat it is bit different situation. Yes, one in 20 peasants can hit a dragon, even if they should not - because dragon will not drop from one peasant hit, plus he will obliterate attackers in next round anyway. Such assumptions do not transfer well to skill checks.