After re-watching the episode, I think it would definitely make sense for Burnham to want to remove herself from the timeline (apart from the wider mission) to allow Spock as normal of a childhood as possible for a little boy who has enough obstacles in front of him already, and so he could receive all the love Amanda wanted to give him.
But in the adjusted timeline, each DSC crew member would still potentially be living their lives independent of one another (for the most part, anyway), just like the crew of the Time Ship from VOY's "Year of Hell" episodes after that ship was destroyed. Burnham included.
To further support the idea that DSC's unique capabilities are the key to this, I cite the Mirror Universe, where we know that life goes on as usual in the Terran Empire - no galactic threat, but also no spore ships, because the only 2 spore-driven ships they had were destroyed. So there was no vehicle to import the galactic threat.
Without knowing that Discovery would receive a 3rd season, I believe the writers might have written in the components for the finale within the Red Angel plotline, and there's no reason to think that that plotline has to wrap up this season. DSC (and Burnham) can live for another season or more, but this might loom for some time to come. Time will tell.