Finn has no family. Or rather, he has no family that matters and which he can return to. He has heard too many tales around base about any of that. Members of the resistance have had children taken by the first order and most just don't want them back. They know what they will have become. Finn is clearly the exception among murderers and thoughtless drones. Part of him wondered but he shut that down after a few weeks. He heard Poe speak of his family and siblings and a life Finn could never fit into even if he could find them.
He can only move forward with his new name, new identity, and new place in the world. He was not a good soldier for the first order but he still has training and he can put that to use around camp. When young teens turn up at random bases Finn can teach them how to hold a gun and then how to respect and fire it. He can teach them order and discipline and respect. More importantly is that here he can find the ones who are not meant for that life and direct them elsewhere and that is amazing. There is always another option with the resistance, another way to make yourself useful.
No one is declared obsolete.
Poe offers to find him something else to do but this works for Finn. If anything it means that he did not spend over two decades with the first order for nothing. It means the tears he shed silently behind the mask were not for nothing. It means the skills it took blood and sweat and even more tears to gain will be put to use to end the institution that taught him them. That is worth it all.