I don't see this being the only way as any sort of benefit. Levelling up is something you can do in downtime. If you want complexity here's the best way to put it in.
By "downtime" do you mean player downtime between sessions or in-game character downtime?
Personally I'd like levelling up to be done at the table, such that play can continue once it's done...and thus, I'd like it to not be complex. Feats are awful for this, as I learned in 3e, due to not only having to choose them now but also having to worry about the current choice's effect on potential later choices.
Arcane spells learned at level-up are random (i.e. whatever your trainer hapened to want to teach you at the time), which neatly does away with the time it'd take some players to choose.
But game mechanical should be a part of it if you have large complex rulebooks. And the problem with 1e is that equipment isn't character.
Equipment isn't all of character, but there's no reason it can't be some; and equipment inevitably comes and goes over time in 1e due to its destructability.
If your mechanics don't show individual character growth then what's the point of them other than for a tabletop wargame? And they just show class growth in 1e with people being cookie cutter members of their classes mechanically. It's only loot that shows character growth.
And personality, and played history.
I've got two 10th-level Fighters out there. Both started around the same time (one in '83, one in '84), and they're mechanically very much the same other than one has a specialized weapon and the other does not (we didn't have weapon spec. in 1983 and I decided not to pick it up later). They're also both Human males, and both are still alive and active today.
Right from the start, though, their personalities were quite different - '83 is a practical problem solver, fairly quiet, and started out looking to get rich; while '84 is a loud vulgar-mouthed PITA who hates Mages and strongly supports the Fighters of the world. And their in-play histories have made them even more different. Yes they both got married during their played careers, '83 to a long-time running mate (another player's PC) who later turned out to be - I kid you not! - a princess in hiding; '84 to a long-time NPC partner-in-crime; but those marriages also went different ways: '83's marriage has been, to say the least, rocky (they're literally living on different worlds now, trying to reconcile long-distance for the whatever-number'th time); 84's is doing fine and they're currently building a stronghold together.
End result: someone seeing these characters in play would have no idea that under it all their game-mechanics are nigh-identical. And that's the point: not only are game mechanics not everything when it comes to defining a character; there comes a point where their input doesn't mean that much at all.
Oh, and "84" is Lanefan, my namesake here.
"83" started out as the captive engineer found in the lower level of A2 Slavers' Stockade.
Out of curiosity what do you do to stop it? Soulbind the items so when the PC dies they vanish.
Not at all.
But I try to encourage players to make wills for their characters, and it's kind of accepted that you don't will things to your own other characters - particularly ones that don't even exist yet! - unless there's a very good and logical in-game reason. For example, a player once brought in two brothers at once; obviously, they willed their possessions to each other, and that's fine.
And - again perhaps obviously - you can always will things to your family members etc., but by then we'll already know if said family members are adventurers or (far more likely) not, and their class-level-etc. if they are.
