Basically, if you've got enough personal power to just say that you're a monarch now and force people to go along with it, you also have enough personal power to choose which kind of monarch. Y'know, hence "Emperor of Haiti." The post-independance states of the Americas are all colonial regeims, ie their claim to power is not predicated on a succession of previous, similar governments going back for forever, the kind of thing that would obligate a Bourbon and make them want to call themselves King of France. And indeed they were all predicated on fairly explicit repudiations of any organizational structure that could claim anything of the kind.
Mexico or Brazil aren't like that. They are the direct political continuations of the earlier colonial government, the colonial government of the nations they had just asserted their independence from. Similarly-straightforwardly-successionist movements in Europe would be able to generically tie themselves to a previous government of the area, and just say "screw it, this is the Kingdom of Pannonnia now," but as mentioned, the independant colonialist states where not going to tie themselves to anything like that, because it would sort of implicitly obligate them to upgrade the natives from non-citizens to at least third-class-citizens.
So, no historical obligations to one title or another, and if you're making up a new monarchy on the spot anyway might as well go big, y'know?