I think Mon El is here to stay. I'd be really shocked if they send him packing at the end of the season.
Chris Wood's acting was very good this episode (Melissa's is always good; especially in those emotional moments.

). I really could see that he did love Kara very much; whatever his heroic tendencies, or his understanding of what being a better person entails.
I don't agree that he wants to stay back from a moral perspective rather than a romantic one because his whole explanation in all of his conversations was a. he wants to be a hero because he wants to spend his every moment with Kara b. He wants to be near Kara because he believes Kara makes him a better person.
Both are problematic in that, I'd prefer people to have motivations beyond romantic love; have career aspirations and goals; and a character outside of the fact that I came to this planet, I met this girl, I liked her and am inspired by her, and now I want to spend all my time with her, helping her, okay, but yeah. Oh, and before that I was just focused on having a good time.
Anyways, even if you consider that his stance to stay behind was moral, I think something more moral, or I should say, nobler would be for him to work for his people; to work towards settling his planet with refugee and scattered daxamites and then work towards a better civilisation for them; may be ending in a democracy?
After all, it is not for nothing that heads of states (or activists) and such who have changed an entire country's future are slightly more celebrated than cops, and even military people even though they are individual heroes. The scale and magnitude of the effect/reach of a head of states' actions would be more far reaching that most individual heroes.
Considering that at least until his mid twenties (if Daxamites age the same way in Daxam as we do here in Earth), he lived off the fruits of the labours of the oppressed in his planet, it may also be something of an atonement for him. He is not a layman. He is a prince. (It's not the same as blaming white people now for slavery and Jim Crow, because those were before the person's time). (Not to mention that M'gann, a lay person, did so much more without outside input or inspiration.)
The show could actually go with that while including Kara. Next season, Kara could leave earth behind to help Mon El; lead Daxamites onto a new future.
It'd involve both parts of the identity the show has focused on this season--> Kara Zor-El (Supergirl) and Kara the lover. She would serve as his support system, inspiring him when needed, and at times, may be his people too, fighting with him when needed, and arguing with him when she thinks he is straying--all of which she has been doing very well this past season. Just like all the great women who have been wives/partners of heads of states and revolutionaries have done.
There would be great potential in this storyline (provided handled properly) because it might involve going to hostile planets to save some contingents of aliens who may have been sold to slavery, going to another planet where folks have settled more or less okay and trying to convince them why going back to Daxam is such a great idea, dealing with special-interest groups that are in it for themselves for their own sake and so on. You could have action and superheroics, intrigue, diplomacy, drama and comedy as well.
And, as said before, she could inspire not just him but his people as well, so she would have as a wide range as in this season. Just replace Lena with some other woman; or man. May be his cousin or a scion of another noble family in Daxam.
Her moving from earth shouldn't be a problem. As far as I know people do move locations for romantic love.
Or, they could just take a 100-year leap at the end of this season (done all the time in Hindi TV shows when they need a change), so that Alex, Winn and James will all have been gone (happily and in peace). J'onn could get a message from M'gann that her resistance out there in the green planet is working and they have a considerable base there and he could go back there to help with it. May be, there could also be some hidden green martians in other planets who could be found, that he could have them as a basis for another Green Martian civilisation.
In the third season, they could have some scenes where Kara reminisces about her time on Earth (whatever her reason for leaving) and some scenes with Alex, Winn and James... And, then, by the fourth, they could completely do away with that and focus only on Mon El, Kara and the people.
Considering just how important public service is, and how strenuous, and how less it's appreciated really in the stories, it'd be a good story for the youngsters watching too.
And if they still want diversity and inclusion, they could have a new LGB or T couple or person among the Daxamites, and a POC or two.