It's just an idea I thought of.

Skyrim is a great game, but for all its MQ is worth, downloading skimpy armors seem to be a better investment at times (mostly because of the dragons)

I just got to thinking that, perhaps it's possible to have MQ plays itself? So while we frolick with birds, something happens far away. Just to add spice and feel that there is a dragonborn somewhere doing its job without that dragonborn being you. Dragons also can't give us soul, and we can't absorb Shouts, but that's not really important.

Most things in Skyrim MQ should be pretty reproducible, such as Greybeards' shout. The wars are also mostly about enabling and disabling stuff in town.

Anyone here experienced enough with quests can give advice whether this is (remotely) possible or not?

Well, I'm not particularly experienced with quests, but I imagine you would have to do something like take all the trigger events in the existing MQ that cause dialogue changes from NPCs or alterations to the world, and attach them to a new quest which is related to the player's actions in some way but isn't driven by the player actually being the Dragonborn. Perhaps a new quest which sets events off based on the player's level? You could also create a handful of scripted battle scenes showing events from the MQ(Western Watchtower, Kynesgrove, etc etc) which would only trigger if the player is in the proper place within the appropriate level range. You'd also have to jigger about with the factions to make sure that the player isn't constantly under attack from Dragons, only when they're already attacking towns, and have some mechanism in place to "clean up" Dragons a certain amount of time after they spawn, to mimic the effect a Dragonborn player would have on their population.

It's certainly not a small job.