That there is no objective proof doesn't mean the balance of probabilities is 50/50 though. Maybe 99% would be more accurate.
We can't prove Socrates, Thales, Pythagoras or numerous other Greek philosophers existed, but that doesn't make their existence 50-50 (which would make half of them purely mythical).
It would matter far less if there were no historical Socrates (simply Plato) or Thales, or Pythagoras (centers around which reports of early philosophical ideas are gathered) because we have a larger or smaller view of the relevant ideas, which is what we're really interested in; an historical Jesus is interesting because of the claims no so much that he was a human to whom magical feats are attributed but because he was also at the center of one of the world's largest religions on the basis of promising postmortal existence, and who,if he was as important as claimed, ought to have a clear biography but has only a sketch, a devised bio and three variations on the devised bio; ought to have been mentioned somewhere in his lifetime but isn't; ought to have had a central message but doesn't. And so on.
I'd say the contradictory narratives are better evidence that people are backfitting around a historical figure.
Let's just agree, then, that both views are possible.
The biographies of Muhammad have all kinds of competing information also.
The Qur'an was assembled as 'the sayings of Muhammad' two hundred years after his death, and western Muslim scholarship, where it's permissible to talk about such things, has no doubt that if there's any wheat in there, it's buried under a mountain of chaff. Unlike Jesus, there does appear to be at least one contemporary and independent reference fitting Mohammad, though.
For a pure myth you'd at least start with a single narrative, a real person on the other hand requires people to create their own, hence diversity.
If you've ever looked at Graves' The Greek Myths, you'll know that nearly all of them have multiple versions, different names for the same and new characters, and so on. It's not even clear that somewhere way back there ought to have been a single first tale, instead of an evolving and fusing and dividing of tales. Your argument ought to be stronger for a character invented between, say, 1 and 49 CE, and if there was a story, Paul, if his claims to have persecuted Christians and to have met disciples are true, ought to have had a reasonable look at it; but writing in the 50s CE he knows almost nothing of an earthly Jesus and cares even less. And the author of Mark knows little more, but sets about creating a bio, the only one we have, regardless of whether an historical Jesus had died 45 years earlier or not.