the Roman Constituion didn't allow it?

I don't know very much about late antiquity, but this statement needs addressing. There was no Roman constitution, written or otherwise. There was no document that outlined the structure and function of the Roman state. Scholars have gone back and forth for a century and a half on the question of whether the Romans had a concept that we might call "constitutional," with the most recent study appearing a couple years ago from Benjamin Straumann, but the consensus opinion is that the Romans did not understand anything that we can really justifiably call a constitution. The Romans did not have constitutional theory in the way that the Greeks had it, in that Greek political philosophy described, but did not define, political systems. Cicero is the closest you're going to get to that, and any headway that Cicero made on the theory of government was snuffed out by the civil war. The Romans did not even have a body of law that regulated how magistracies or functions and institutions of the state were supposed to behave. Custom, mos, theoretically laid out how the state was supposed to work and how people were supposed to behave within it, but at the best of times mos was unclear. Customs were not written down, and referring to "custom" typically amounted essentially to the public justification of an action because somebody else had done something reasonably similar in the past. Such exempla were squishy at best, and appear to have been inventions of the tradition quite frequently.

No law forbade the use of the term king as a title, not among Romans nor anyone else. No law, after all, defined consul as a title, nor did any law even make clear how to pass laws--that the plebeian assembly tended to pass laws by the first century at the expense of the centuriate assembly, which still had the ability to do so, is a result of social factors, not legal ones. That king was not used as a title at Rome has only to do with the fact that during the Republic there were no kings at Rome.