I think they are developing the characters nicely and you can imagine them being a crew for future exploration post-war. However, the plot lines do point to the fact that each may have some serious problems adjusting to life post-war:
Lorca - heroic leadership but also crazed from blowing up his previous crew and being tortured by the Klingons and pushing the rules with the Disco crew. He could be relieved of duty at anytime by the admiralty of Star Fleet.
Ash - heroic soldier but crazed by being tortured by the Klingons and of course the lingering suspicion that he is actually a genetically/surgically altered Klingon.
Stamets - heroic scientist but crazed by having Tardigrade DNA injected into him and having had too many trips into the multiverse with the magical mushroom spores.
Burnham - heroic efforts all around but of course there is still the matter of the life sentence for mutiny.
About the only…