I have no idea if something similar has been created or requested already. If so, I didn't find that mod or topic. I also have no idea how to create a mod or anything, just having an idea. Anyway, we all know how shrines work. They add certain blessings depending to whose shrine it is and remove the others, though that only works at non-daedric ones. I somehow had the idea that the player could be enabled to worship or pray to a god of his choice, daedric ones included, maybe even alduin since some refer to him as a god. In turn for worshipping or praying to whatever god you chose, you'll get certain benefits. Different ones per each diety, similar to the blessings at normal shrines. Though those would only kick in after a few days of worship or prayers, maybe have them increase up to a certain point if you keep praying to them. Chosing to worship a Daedra could come along with not only benefits, but also drawbacks. For example, maybe have ghosts or similar things haunt the dragonborn if he / she choses to worship sheogorath? I have no idea for worshipping Alduin or if that even would make sense. Being enabled to use his meteor shout from the beginning of skyrim for as long as you worship him, increase in shout power? I figure this worship could either be done at the shrine of each diety or by adding altars or something similar in player owned homes where you could select a god and then pray to them. To stop worshipping and have the effects of it disappear, simply stop worshipping for a while. In short, it'd just be a way to increase the shrine benefits by means of worship while also adding daedra into it. Same or similar benefits, one diety at a time, in order to keep the bonuses up you'd have to pray to them / worship them once a day or whatever set interval. There are NPC priests and worshippers after all, why not let the dragonborn possibly do that too?
