it's likely that he exists independently of mortal belief
I rather not jump to exceptions. Occoms Razor. I don't subscribe to idea of CHIM either. Although I do realize many people take it as lore. So here we might have difficult conversation. So maybe it's best leave it at that and agree to disagree.
We've never had any proof that Reman Cyrodiil became Ebonarm after death. Sure, he was worshiped by some as a hero-god and god of war, but nothing has ever positively linked the two besides a similarity in their names.
Yeah. I would argue same is with Talos, as it's the faith of mortals which formed the legend and gave body to it. But we already disagree with that.
and was able to wear the Amulet of Kings and light the Dragonfires
Again. I don't subscribe to idea that being able to wear amulet of kings is indication of one being dovahkiin and that refers to separate thing. We also have Michael Kirkbride stating that Alessia wasn't able to absorb dragonsouls. Now it's just one person, but it means that amulet of king thing is not the same as being Dovahkiin. And also draws distinction between the two.
but were instead blessed by some other Time Dragon
Why to use one example and assume every examples must be like it? See, here is where I have the problem. "Being blessed" seems to be a trap of religious convolution and mistake on common parlance part. In rl we also refer to talented people as "gifted" but it doesn't mean that someone gifted them their talents. They are simply born that way.
That's not to say that I disagree with the idea that some Dragonborns are created by accident or chance, rather than divine will, but it just needlessly complicates matters when you try to link all of the known Dragonborns
Why to try to link those in the first place? Yes when you try to build even more unsupported structures on pre-existing poorly supported structures you run into problems. Although that's common in lore community with CHIM, Dragon Break and other stuff like that. While I can understand Dragon break due it's necessity. Dovahkiin / Dragon Emperor relation does not have such necessity. And it's easier to think that those are separate cases. Or to assume that perhaps there is some relation but to avoid pulling stuff out of thin air.