Most things in life are not random. Vaugn did not "roll a nat 1" -- she went out there when she was not up to the task. Yes, she was an amazing athlete, but she is past her prime and did not want to accept that. You see that a lot in sport.I'm going to throw in a related concept - if you're an expert in something you should (almost) never fail. Some systems explicitly code this, but others leave it up to the GM. Can experts fail? Yeah, just yesterday or the day before one of the ladies at the Olympics broke her leg skiing. She's one of the best of the best since she made it to the olympics but she still rolled an nat 1 on her run. However, MOST of the time, it would be silly to make your Osiris Cleric roll Arcana on knowledge about Osiris; especially if the barbarian can roll a nat 20 right afterwards and know more about the god than the god's own cleric. One exception would be high level secret knowledge. Let's say you had a religion where the lay folk and the low level clergy had one truth about what was going on and the high level clergy knew what was REALLY going on. Then arcana would make sense to see if your person came across some secret knowledge one day while they were in the temple.
To bring it back around to your original question - while I prefer a static DC - a wall should not get harder to climb the more I've adventured - I also wouldn't ask my ultra-nimble fighter to roll OR I might set the DC to 1 (allowing for an epic fail like that olympian). Everyone else, especially the wizard, would have to roll.
It is actually too bad few games capture that part of it. I bet lots of old adventurers would bite it on "one last run into the dungeon before retirement."

