i'll explain that, well you see. when the king dies, the natural heir doesn't always become the king(the king can choose someone else, but if he doesn't the natural heir becomes king). there is a ceramony that needs to be done for the heir to ascend to the throne and remove that title of prince and gain the title of king. since all the saiyans died and there wasn't any saiyans left to rule, vegeta didn't really care about being called king and forgot the ceramony. besides, there weren't anybody left to do the ceramony and no one knew the proper way to do it. vegeta never really thought about being king because he had so much other things to worry about(his life). later on, he slowly stopped calling himself prince after trunks was born. he just didn't care about him being ruler anymore, afterall there was nothing left to rule since 99.999999% of saiyans were dead.
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