Ah, I assumed we were talking about Jupiter based OT systems - which are outperformed by their newer cousins (like eg-walker). Like you say, these use a different data structure to transform changes and that's why they're faster.
> My reasoning is that CRDTs require idempotence and commutativity, while OTs do not.
The only property not required by a centralized OT system is the OT TP2 property. Ie, T(op3, op1 + T(op2, op1) == T(op3, op2 + T(op1, op2)). Central servers also give you a single global ordering.
If you discard TP2 and add global ordering, does that open the door to new optimisations? I don't know, and I certainly can't prove the absence of any such optimisations. So I think the burden of proof is on you.