What you can do is go to Admin -> Plugins -> Question types -> Manage question types, and enable and disable question types for everyone.
When I implemented that (many years ago), I did think: "should we make this be controlled by a capability, so you can give permission for some people to use a question type, but not others." But then I thought "No, that would be too complicated". But subsequently, we have seen capabilities like mod/quiz:addinstance, and block/html:addinstance introduced for exactly this sort of purpose for other plugin types. So, we could re-consider whether to use this pattern for question types too, but someone would have to implement it.
So, there is not currently a way to do this. Sorry.