I wish they'd actually finish the protagonists' story each game before moving onto new protagonists, instead of just cutting stories in half and passing the second halves off to new protagonists, despite lack of closure for the old protagonist and lack of personal investment for the new protagonist.
For example, I may not like DA2, but it's pretty clear that one was rushed to release and there were a lot of loose ends dangling. The Exalted March DLC was meant to wrap up those loose ends and bring closure to Hawke's story, but the DLC was scrapped and many ideas moved over to Inquisition, where the Inquisitor got to complete Hawke's story and take over Hawke's friendship with Varric and rivalry with Corypheus, despite having no personal history or emotional investment with those characters. (And I say that knowing that I benefit from the Temple of Mythal being carried over to a game where I could play an elf.)
DAI was also originally supposed to be twice as long, but the devs said they basically cut the story in half and the first half is what we got in DAI, while the next half will no doubt be covered next game. A lot of the story meant to be covered by our Inquisitor goes to new guy/gal, especially the "Stop Solas" part (whom I hear Weekes has said emphatically said, "his story will end next game"), despite how the Inqusitiors is the one with all the personal history and potential emotional investment in the guy. We spent all of DAI slowly getting to know Solas as the Inquisitor, then Trespasser boldly revealed his identity as the Dread Wolf to our Quizzy, then set up their antagonistic rivalry, with Solas vowing to tear down the Veil and the Inquisitor vowing to stop him... then ZOINK! Some random stranger who wouldn't know Solas from a hole in the ground is the one who's going to stop him next game?
Again, Quizzy was the one to stop Corypheus despite Hawke having all the history with him, and now the next protagonist will no doubt stop Solas despite the Inquisitor having all the personal history and potential emotional investment in him. (Whether friendship, romance, or even "I've been waiting a long time to give you this knuckle-sandwich.")
BioWare can do whatever they want, of course, it's their Intellectual Property, but I think it'd make for more emotionally compelling and engaging stories if they'd let protagonists cash in on the emotional investment they put into their interactions with companions and antagonists in their games, and let them finish their stories and defeat their baddies with emotionally satisfying conclusions.