And how often are you going to be climbing in combat

Not often at all, that’s why I don’t think it’s the reason they picked centaur

The fact that you can have a Tank with Mounted Combatant riding you is very useful to a normal wizard build.

It’s definitely a valid approach, but it’s worth remembering that player centaurs are only medium-sized so the rider actually loses the advantage against medium-sized enemies that Mounted Combatant would otherwise give them. It’s not useless by any means, especially if the centaur takes Protection (although that would require grabbing a fighting style one way or another too), but I’d be surprised if it was all that much better than just having the rider on a regular horse and the wizard not in melee. The wizard does still have to actually pass the dex saves, after all, and this one is not going to be doing that very often

The thing about centaurs requiring their own mounts to keep up is pretty damn funny