Should everything scale with level?
I've seen people on several occasions say that pretty much, everything should scale with level. A 10th level Fighter should be able to jump farther, last longer, and have a better chance of opening stuck doors or dodging traps. As one person put it recently, the fundamental assumption of D&D is that your character improves and gains power.
Except, of course, that the original D&D books have almost zero improvement of abilities or additional powers outside of spell casting. Everyone increases their hit dice, which are tied to saving throws and combat ability in addition to basic survivability. Spell-casters gain access to higher level spells. Fighters get to fight more opponents simultaneously. And that's pretty much it. The books list several mundane abilities: learning languages, gaining henchmen, mundane acts like searching for secret doors, surprising opponents, spiking doors shut, and yes, opening stuck doors and dodging traps. None of these abilities improve. Movement rates don't improve, either, nor does carrying capacity. I think it's notable that these abilities are mundane. D&D characters are ordinary people with one trick, and only that trick improves as their level increases.
This wouldn't matter, except that those in favor of scaling all abilities to level always get bogged down in how to scale challenges to level as well. If a 10th level Fighter can jump a 50-foot chasm easily, then you need to design areas with 100-foot or 200-foot chasms, to increase the difficulty. Ordinary doors become too easy for 10th level Fighters, so you need special "extra-stuck" doors. The end result, if done right, is that characters face exactly the same difficulty at every level.
In which case, why jump through all those hoops? Make all stuck doors equally difficult for all characters. Occasionally throw in a barred or locked door, or one that's been bricked up. The only things that change are the monsters and magic.