I think that has more to do with the fact that winter is coming and you can't exactly fight an offensive war in a harsh winter and it's a logistical nightmare to keep your army fed, warm, and keep the morale high. We don't know the extent of winter in this universe, but it sounds a lot worse than a normal winter and we know how bad weather has stopped much better operations in real life.
Also, there's a lot of people going for the throne so it's important to get there and win over the people as the true legitimate heir. He knows about Dany gaining a lot of support in Essos and he doesn't know about her issues over there like we do (insurgencies are always fun) so he needs to unite Westeros ASAP.
Even if he becomes King, I can't see him lasting for too long besides fighting off winter and the white walkers if they ever come. He's always felt like a middle man and not the end game to me. Melisandre is using him to spread her religion (possibly bullshit) and will use anyone else she can if it furthers her cause, whether that's Stannis or not. I just think Stannis went from a just character that abides by the law to a guy that is slowly being perverted by a woman using temptation and tricks to win him over and advance her own beliefs on the rest of Westeros at the expense of Stannis's popularity. All the shit he's done will come back to bite him at some point. Melisandre is like one of those archbishops back in the Medieval Ages that would turn their kings into their puppets. Melisandre doesn't have as much power as them yet, but she's pulling a lot of strings while letting Stannis feel in charge.