I'm not offering a solution or even a complete analysis here, just babbling to help me organize my thinking on the topic.
Something I noticed before about adventurers in most D&D campaigns is they often, and quickly, attain individual power that can literally topple nations.
"You and what army?" becomes, "Aw, you sent an army, how cute!"
This is especially true of magic users.
The commoner / nobility divide is not even considered in AD&D's rules.
It can be a campaign assumption. Standing Bear's Hundred Town campaign, where I learned AD&D, you started as an orphan the day the orphanage kicks you out. You got a copper piece, a dagger, a set of clothes and a lump of goat cheese. Oh, and enough training to be a 1st level character of your class.
This, I am sure, influenced all our gaming and we were never nobles.
Most of the other fantasy rule sets really mention it either.
Stormbringer, using the Chaosium Basic Role-Playing System, had mention of nobility. Much to the frustration of our GM, we had a rare talent for getting lucky on the nationality and origin table. (It turns out that Scott was using that table wrong, it was for randomly generating an NPC, the players were supposed to be able to choose the character's origins. He just didn't know he was supposed to forbid origins that didn't fit his campaign...)
Warhammer certainly didn't make most characters noble.
In GURPS you could make a noble, but it costs valuable points you could be spending on something keeping you alive.
Commoners are not supposed to be able to have access to such power as to topple the legitimate government or challenge the divine rights of kings.
Government was something we just didn't do for most of our gaming. We didn't even ignore it, there simply wasn't any. Well, it might have been there, but it didn't rise above subtext.
Even when I added government, much later, it wasn't near intrusive enough and it never really affected the players.
Feudal governments are of the "a place for everyone and everyone in their place" variety.
The rise of a middle class and commoners getting rich as nobles really destabilized feudal reality.
Adventurers would certainly be part of this. They're powerful individually and often become insanely wealthy.
This is not necessarily a world ending problem, Elizabethan England survived merchants being richer than the nobility and the United Kingdom spawned and outlived the East Indian Company, which had nation state power.
The nobility could be faded into the background, like the Junkers.
The GM will have to decide how the existence of adventurers is handled.
I've been using less medieval model for the fantasy settings I've been using because it's easier and closer to how we think of government in our egalitarian American culture.
Plus, there's always that Divine right of kings in a world where you can physically speak to The Gods. How can you lose with God on your side? How would your little rebellion go if the cleric found themselves powerless because their deity says King Incompetent the Third shall remain king?
I have a model, it just needs fleshed out. Some of the work won't really be complete until there's players, but it keeps me from eating my own mind.