They're certainly not unsuitable, but they have a tendency to take observation/realization/grasping/proving as an instantaneous process. In most people's regular understanding of logic, however, this is false. There is a process by which new data and new conclusions from that data are drawn and made available to you.

So ultimately, if those things matter for either UX of mathematics or for actual mathematical content is a large question, but it's fairly clear that if you need to capture something closer to the actual dynamics of knowledge/learning/understanding then you are sunk when you base your foundations in set theory.