If someone changes type they will do a whole new type rating course and do lots of things differently. So that is a spurious argument.
If the fleet has some with RH tiller and some without, that makes sense.
I find it interesting that you think that turning a tiller puts someone "in charge" of taxiing. In a busy ground environment it actually makes more sense to me to have the inexperienced guy driving and the CA doing the navigating. On my type which only has a tiller on the left I have lost count of the number of times I have had my workload through the roof due to trying to taxi as well as sort out where we are going because the F/O has failed to read the plate properly.