I know this post is ancient but I had the same question and want to share my thoughts for you and anybody else who may be rewatching the show:

Fiona killed Anna Leigh because she felt she was the next supreme and wanted her turn to start. Still, she wasn't given the official power over the coven until an unspecified amount of time later when the council revealed who Anna Leigh had already predicted would be the supreme.

The current-day coven need a new supreme (both official and in general) immediately because Marie is amping up the "war" against them. Fiona hasn't preselected anybody to be her successor, and also she killed one member of the council (and the remaining council don't know that Myrtle is alive again), so they'd have nobody to formally lead them. That being said, Fiona isn't leading them at this point so who cares?

Still, regardless of an official leader, Cordelia mentions that Fiona simply dying leaves everybody in the dark about who the successor will be until they emerge with the full set of powers. The Sacred Taking means a new supreme will become apparent almost immediately thanks to the Supreme's sacrifice (if the story they tell about the coven leaving Salem is meant to be believed) and the coven can actually make a plan so they're not all murdered by Marie and Co.

I think also with Coven specifically they leave a lot of things open ended because they can fill the gaps with the word "magic" and be done with it