Gammadoodler
Hero
Except that you, and you alone have decided that centaurs fit in as PCs and what the centaur can do in this scenario (again ignoring that your judgement call here conflicts with published rules).Well, I don't think there would be a "mess". As long as I'm clear ahead of time how I would rule (and I would be) it's not my responsibility to make the environments or scenarios fit the PC.
If I make it clear to the players that I'm running an urban campaign and somebody comes to me with a wood elf, they don't have a leg to stand on when most fights don't occur in natural environments. You could say the same about centaurs. As long as I'm clear they don't have a hoof to stand on when everybody else can climb that ladder.
If your player says, "hey wait, there's nothing in the rules about being incapable of climbing this thing".. they're right. It's something you made up. You get to own it.
(Note: the ruling here also ignores any potential class features, so potentially your 20 strength barbarian rogue centaur is less capable of climbing than your 8 strength wizard. )