He held firm to the title, why exactly?
Because of how the North would react to a foreign queen. That's it. At no point was he ever interested in being king.
Matter of fact, the very first meeting he had with Dany, he told her how insignificant titles are. How they're all "children playing at a game".
Then in the cave he said the main reason he was refusing to bend the knee was because the North "won't accept a Southern ruler".
Only after she pledged to help him....
for nothing in return....did he feel comfortable giving up his title. Because that showed him she would be selfless.
So....yeah.
Fred.