That's not compromise, that's complete cultural surrender.
Since when was 'submission to elven mages' the complete cultural summation of the Dalish, let alone a good aspect of their culture?
Ignore, of course, that I threw out a number of potential options the Dalish could play a change to the Keeper system, some of which didn't even contest the continued role of mage-rulers.
You're asking the Dalish to give up one of their few cultural traditions all clans we've seen so far have in common - and what does the other side give for that?
Depending on what the compromise is on the Chantry side? Potentially a lot.
No longer being considered dangerous apostate harborers is the most significant, and with that comes thus no longer needing to be nomadic to escape from Chantry enforcers coming after the un-regulated mages. No longer being nomadic means they can create settlements. With settlements come transition from subsistence living to societal development: stable population bases, record repositories to keep and preserve lore beyond suspect oral tradition, and enduring political relations and (and thus alliances) with local interest groups to build political allies and advocates.
And that's just if the Templars (or whatever their re-named equivalent post-Inquisition) mage-security-wing of the Chantry are satisfied with whatever accomodation are done. Which depending on the deal, doesn't even necessarily necessitate an end to mage-keepers if other compromises are made- consider the proposal of a Templar-affiliated observor who's role is to watch and observe for maleficar tendencies, which will reduce ignorance and misinformation of what the Dalish mages actually do.
If reconciliation with the Chantry as a whole is achieved by changing mage supremacist leadership philosophy- and considering that one of the historic fears of Southern Thedas is the fear of mage rulers lording over mundanes, the Keeper system as-is doesn't help reassure any political partner- a whole world of political options for the good of the Dalish starts to open up.
International legitimization. Political normalization. Even the creation of a Dalish polity that can actually claim to represent at least some regional Dalish, and both negotiate and be negotiated with to raise grievences and moderate tensions with the Chantry and Chantry-deferring countrires. One of the best ways the Dalish could slow or stop their cultural dissentigration is to re-create a unified polity, and the best way they can take an actual leadership role for city elves across Thedas is if someone has the relations and the influence with the Chantry to bring their attention to city-elf issues as something other than a strictly national concern. The only polity with international standing that they could hope to piggy-back that sort of reach off of is the Chantry itself- and better relations with the Chantry would benefit Dalish clans wherever the Chantry has influence, which is to say almost everywhere that matters.
Make no mistake, and don't straw-man me as if I'm saying simply changing the Keeper system is sufficient. It's not, and there are a lot of other issues to be addressed. But what the Chantry might offer will, of course, depend on what the Dalish offer in-turn. Changes to the keeper system- a system that doesn't actually select the best or most knowledgeable or most lore-cogninant elfs to the role of cultural leader for merry bands of cultural preservationists- is something that is entirely in the Dalish's power to change, and has significant influences on their relations with the most necessary institution for rapprochement.
When negotiating, offers need to be something you can deliver and something the other side wants. Political changes to their leadership caste is something the Dalish can do without any outside help. Mage policy is also one of the very few things the Dalish can offer that the humans actually want.
If not that, what would you offer as a compromise that might entice the Chantry to the negotiating table?
(Besides such low-hanging fruit as, say, allowing Andrastian missionaries to visit the tribes.That might be good for the Chantry, but it doesn't do much for the Kingdoms.)