If people want to use the existence of god to do science they'd have to prove the existence of god and then apply those properties. However, the onus of proof in other endeavors is rather different. I've never contended that using god to do science is sensible, or that assuming god exists for the purpose of verifying some scientific fact is useful.

For instance, in theology it would be a rather pointless to argue that you can't prove god exists, therefore you shouldn't study the divine at all. Similarly if you are studying Aquinas and metaphysics, arguing there is no soul will not lead to understanding of the philosophical implications.

Furthermore, there are countless examples where assuming something is true and studying the consequences is very useful, particularly but not exclusively if a contradiction arises leading to a refutation.

In any of these above, assuming the non-existence of god would be pointless and would curb discussion. Just because its correct for science doesn't mean it's correct in general. If something is not known to be true or false there are benefits to looking at the consequences of both truth and falsity often with a context dependence. For example P = NP? is an open conjecture. Looking at the implications of P = NP could potentially lead to a refutation of P = NP by contradiction. Furthermore if P = NP turns out to be true, having studying the consequences in advance, we would have a huge number of immediate results, and a surge in research. Likewise looking at P not equal to NP could lead to a refutation by contradiction, or new results that follow from P not equal to NP. In computer science the correct approach is to study both possibilities.

Since its so often the case that the correct approach is to study both possibilities, I don't see why in this particular case its wrong to study both possibilities calling one study Theology and the other study Science. Particularly since that is what eventually happened in the academic community.