Assuming the Qunari invasion in Tevinter is the "new epic adventure" ® a time skip of 10-15 years for the new story could be very likely.
If there is a Qunari invasion, there will be people demanding that Sten, the HoF, Bull, Krem, Dorian, Isabella... al make a comeback... Which would kinda defeat your desire for no more cameos.
If anything, I hope the next Big Conflict™ won't be tackled until the fifth main entry, in order to give the series time to breath.
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they could end up like Shepard in the ME trilogy - forced into an ever narrower character type with each sequel
The blank-slate that Shepard was in ME1 was boring.
The invincible space-marine from ME2 was infuriating.
It's not until ME3 turned Shepard into a PTSD-riddled Pyrrhus that I started to like this character.
(Then again, I had sworn-off the series after the second episode had fallen into the land of juvenile power-fantasies and came back only after I learned that the third episode's conclusion had pissed hardcore fans beyond reason or belief, so I know I'm kinda an outlier when it comes to tastes here)
DA has sort of a "continuing protagonist" with the world of Thedas
I'd say that the series protagonists is the Age, not the whole World.
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The very idea of а leader of such organization as inquisition, gathering flowers in the field and killing bears with his own hands is ... a bit ridiculous and unrealistic.
At first the Inquisition is a fledging organization lacking both resources and manpower.
After Skyhold, well, hoarding habits are hard to get rid off. 