By abdicating, he already had acquiesced, and for him to go back on a promise he made-one he supposedly made in good faith to keep the peace in Wakanda-wasn't a good look for him. That said, T'Challa could've still protected Wakanda-either outside Wakanda-or just go incognito. Why draw more attention to yourself by dressing as the Black Panther and declaring himself as that? He clearly has the technology to look like a totally different person, so why not disguise himself as a different vigilante? Perhaps it can be spun that he was going back to the grassroots and building back up trust with the people first, but that hasn't been explained in the book yet. And maybe him donning his BP outfit is him rebelling and being defiant against the authority of the Prime Minister, but that hasn't been explained yet either. Dr. Ewing has hinted that not everything is rosy politically in Wakanda, but she's devoted way more time to other things.
I definitely agree with you about the need to flesh out the political system, how Wakandans feel about things, and how the prime minister could've been used in this run.