I sometimes play on a profile where the kingdom is not that far developed and I enjoy playing without any gods and not that many items. The dungeons feel a lot cleaner this way and you get to concentrate on only the very basic things.
While i was thinking about badges i had the idea that there could be an option to make runs in which you want to go for, for example, faithless, it lets no gods spawn. So you can't change your mind within the run and you may get a little reward for it. Something like the gold reward for a new badge.
The same could be done for buying items (no shops), Potions (not drinkable or not existing at all) and so on.
Purist won't make a difference because you decide it before the run anyway.
While I like the idea of changing goals within a run ("I won't make it, so I'm going to forget faithless for this run") it would give the possibility to play with dungeons in a basic way which is not dependened on the items or gods you find.