I never felt like changing what one needs to do to earn XP in 1e would break the game
And yet it does!
So there you go.
Without gold-for-XP, the logic of Gygax's game breaks down - because it is
gold for XP that ensures the connection between
player skill and
PC level. Skilled players are better at getting loot out of dungeons - they explore better, scry better, plan better, map better, handle combat (including when to do it and when to avoid it) better, etc. And this skill then manifests itself in the form of levels.
This is also why Gygax is so hostile to Monty Haul play, as that sort of play - by giving arbitrary wealth, and hence XP, to unskilled players - breaks the nexus that he thinks is crucial. (I posted a quote from Gygax emphasising the nexus not too far upthread - my quote was from module S4, but the same stuff can be found in his DMG and is strongly implied in the closing pages of his PHB prior to the Appendices.)
A game without gold for XP no longer has any rationale or structure for the relationship between dungeon-delving, loot extraction, and PC development.
Now, if by "1e" you don't mean the whole game that Gygax presents, but just the PC build and combat rules, plus maybe the reaction table and the rules for doors, then sure - you can take those rules and use them in a completely different play context (where framing is not the output of a dungeon map-and-key, and skilled play is not particularly a thing). I mean, that's more-or-less what 2nd ed AD&D does. But that's not what I would call 1st ed AD&D.