MWI has never made sense because you cannot see wave functions. People are often misled into thinking you can by starting with the double slit experiment, but the wave pattern you see there is made up of millions of particles, while the wave function is characteristic of a single particle, and that pattern you see is still only a projection of the wave function (like its "shadow").

Hence, to say the whole world is made of wave functions is to say the whole world is invisible. How can a world without observable properties explain what we observe? I'm not the first to point this out, but Tim Maudlin and Carlo Rovelli have written similar things.

There's also that whole issue with the Born rule. You cannot just throw out an axiom needed to make predictions in a scientific theory, because then you cannot make the right predictions. So MWI proponents have to reintroduce it but indirectly, by trying to derive it from other arbitrary assumptions. But there is no evidence the Born rule is wrong, and so there is no way to verify any of these derivations, so there's no way to pick between them to decide which is right.

I really don't understand its popularity.