Would you like it doing some king of Dragonic Quest like you walk to a Dragon Statue and it will give you a Quest
i think i already have a list of dragons that can offer you a quest Akatosh Ka-po-tun from lore A Daedric Dragon Tosh Raka - A Khajiit Dragon also From lore
they did that also in Oblivion doing the Daedric quests You worked for the Daedra's and you kill that so you worked for what you killed and i thought it will be cool if they did it in Skyrim
Dragons have power but nowhere near as much as daedric princes have (for the most part(alduin/akatosh)). Akatosh is an aedra and one of the nine divines and his quest would thus be connected to the imperial cult. Tosh Raka is an ascended tiger-man and rules over the cat-people of Ka Po' Tun and is thus closer to the Tribunal of Morrowind in terms of power more than anything, plus he wants to conquer Tamriel once he is done with the Tsaesci. Peryite is a daedric prince that takes the form of a dragon. The daedric princes quests in Oblivion worked because it was only Mehrunes Dagon that was invading and you couldn't do a quest for him. The other princes had nothing to do with the invasion. In addition being extinct for a thousand years would limit your capabilities to reward someone. You probably don't have any artifacts to give away.
I dunno but I think that every shrine's quest should be high level and very very challenging to do, I mean you're after all doing something for a demi-god right? I don't like the idea of a demi-god asking a legendary hero/villain to do a crap task for them. (Unless I'm wrong about Daedra Princes(s).