You're correct Bell was a promoter of Bhomian mechanics. That's not the important part. Bell proposed his inequality theorem as a way to experimentally confirm or rule out hidden variables. Bell's inequality was proven to be *violated* in a famous experiment in 1972 -- which would appear to *rule* *out* hidden variables.
Secondly, that's an incorrect understanding of Everettian mechanics. A branching of the wave function does not happen every time you tap a key on the phone. That misunderstands how decoherence works in the real world. There are not *infinite* possibilities. There is the evolution of the wave function, which is not an infinite possibility space. The evolution of the wave function progresses according to the Schrödinger equation, given the Hamiltonian. Within that evolving wave function, most interactions in our daily life are purely classical! There's no quantum indeterminism going on at every move of your fingers. If that were true, Newtonian mechanics wouldn't work at all, and the Newtonian limit would not be at the insanely high energies it does.
Also, the protests about the extra dimensions, being so unbelievable comes from an intrinsic belief that two branch worlds are somehow a duplication of information or energy. But this isn't true. The size of the universe is proportional to the amplitude of the inverse of the wave function squared for that probability of the measurement. The net sum of the antecedent world's energy is equal to the total sum of branch universes.
In the math, this solution looks far more simple than Bohmian mechanics by a mile, which requires you to imagine there's a whole bunch of stuff that we can't see and can't measure that explains it -- even though the Bell inequality being experimentally violated seems to rule it out.
It's only in the human imagination does Everett seem so hard to believe. The argument for it, isn't that it's exciting like Marvel movies. The argument is it's much simpler math!