Old School characters are treasure hunters, not adventurers
It's common for me to see debates against Gold for XP with arguments like "that reward mechanism turns characters into murderhobos" or "characters become amoral and cynical, valuing money more than the lives of their Henchmen or citizens." To all these statements, I can say: yes, the game can lead to that, but it can also go in the exact opposite direction—it all depends on how the rules are applied.
Why this matters
Old-School Characters are Treasure Hunters because they gain power by recovering treasure.
Advanced Dungeon Master guide on XP awards
Old School Essentials on XP
They go on adventures as a result of this, but that doesn't mean they are "adventurers" a priori, since they don't gain levels simply by "adventuring" (at least in the most orthodox model proposed in OSR spaces).
Characters are not murderers, criminals, or bandits, either. The treasures they loot do not come from temples, vaults, or the personal belongings of civilized settlements.
This gives us a much clearer and more refined view of the role characters should occupy, and how to design adventures and rewards around them.
Treasure as a story engine
From early D&D until Advanced Dungeons & Dragons, there were no rewards for "good deeds" or "overcoming challenges," as it was implicitly understood that characters overcome dangers in their pursuit of treasure, and the decisions leading them there shouldn't be constrained. This is how Old-School style is played, or at least how OSR spaces advocate it should be played.
Some DMs choose to grant experience for good, heroic, or clever acts anyway. This is obviously not a wrong way to play by any means, but my point is that these actions can be motivated and rewarded using the game's built-in mechanics without needing to create new rules.
For example: If the party saves children in danger, rescues an imprisoned person, or protects a village from an enemy attack, those people, communities, or their relatives can point out a lair overflowing with magic items, hand over a treasure map, or reveal an adventure site out of gratitude.
Heroic deeds, treasure, and power should go hand in hand
The point I'm trying to make is that, due to how the game is designed, exponential level growth, treasure accumulation, and having a greater impact on the world are intricately linked—because one leads (or rather, should lead) to the other.
By breaking this reward chain and separating them, we are not only complicating player advancement, but also creating a dilemma for the player: What do you prefer, saving these innocent people and missing out on treasure, or going after the orc lair to level up?
Why can't it be both?
I'm not saying these dilemmas are bad per se; I'm just saying they highlight a friction between the player character and the fictional character, a friction that I personally dislike, as do many DMs. The existence of this "choosing priorities" problem in a campaign can act as an element that enriches the game just as much as a frustrating nuisance. Because of this, many DMs consciously choose to tweak the rules to mitigate it.
These are all valid approaches, but it is interesting and useful to consider the various applications (and limitations) that the Gold for XP system presents for the structure of our world and the adventures we run at the table.