HRE & The Papacy in a 1.091 (and later) world...

Is it just me, or is the first thing you should do as the HRE appoint an antipope, press his claim for the papacy and then set church taxes to High/Free Investure.

Is there any reason not to do this? It seems like a really fast, easy way to make TONS of money. Just appoint popes who all of your bishops will like slightly less than you (they'll have, say, 80 opinions of while they have +100 for you).

This means most bishops in other realms will pay him taxes, most of your bishops will pay you taxes and he'll pay you taxes...

Anything I'm not thinking through completely?

edit: is there a mechanism by which he wont pay you taxes? If he likes himself more than you or something weird like that?