Why, then, don't more people realize that many worlds is correct?

Note that you are using Eliezer!correct, not Physics!correct. The former is based on Bayesian reasoning among models with equivalent predictive power, the latter requires different predictive power to discriminate between theories. The problem with the former reasoning is that without experimental validation it is hard to agree on the priors and other assumptions going into the Bayesian calculation for MWI correctness. Additionally, proclaiming MWI "correct" is not instrumentally useful unless one can use it to advance physical knowledge.

'hey, maybe at that point half of the superposition just vanishes, at random, faster than light'

It's worse than that, actually. In some frames it means not just FTL but also back in time. But given that this is unmeasurable, it matters not in the slightest if you adopt the Physics!correct definition.