The past few posts have been focused on how even experts can occasionally fail, which has been argued to mean that Nat 1s should auto-fail. However, the opposite scenario is also important - should a Nat 20 auto succeed on all skill checks? And the answer to that is an even stronger NO, of course not.

- To take the tightrope scenario, let's walk across a 1 millimeter-width and 1 mile-long tightrope in rapidly changing 5,000 mph winds. The DM sets that DC to 300. Obviously a character shouldn't succeed on that 5% of the time.
- You can jump your strength score in 5e, but if you want to jump farther it's a DM-determined Athletics check. A player wants to jump 2 miles up and 10 miles far. Again, they obviously shouldn't succeed on that 5% of the time.
- Hoard of the Dragon Queen (an officially published 5e Adventure Module) sets a Strength Check DC to 70. Why would WotC use 70 (instead of, maybe, 30) if they wanted level-7 characters to be able to succeed without using magic?

A natural 20 on an attack roll represents the best hit a character can do, which is a lucky or skilled hard hit. They've bypassed the defenses of a fallible creature. Because HP is abstracted in 5e, you could even say that such a lucky hit is actually only doing stamina or armor damage.
A natural 20 on a skill check also represents the best a character can possibly do, but this does not allow them to do impossible things (oft-repeated example is jump to the moon). Physics, unlike creatures, aren't fallible and can't make mistakes you can exploit. If a DC 30 check is defined as "Nearly Impossible," then a DC 35 (or 40, or 70) check should be "Impossible." Not "happens 5% of the time, regardless of whether the DC is 40 or 70 or 1000"