The operative words here are "believe" and "interpretation". There's no testable hypothesis here (or certainly not a tested one); rather, it's a computationally vacuous narrative that some people like to layer on top of the mathematics. This is fine because people don't stop doing actual physics because "well, in many-worlds it doesn't matter". We still want to know how things work in our branch of reality.
The problem with consciousness is that it isn't like that at all. We have a complex phenomenon that is our experience in the "first person". We have an absurdly complex system that appears to be implementing us. And...we're supposed to decide that's not enough? Even though everything else everywhere appears to be a consequence of the properties of its components?
I mean, sure, it's possible.
But all sorts of things are possible. That's a really really low bar to reach to take something seriously. Maybe all the forces work according to the Standard Model, but gravity can't be explained because gravity is actually the Will of God and can't be reduced to a numerical model. (Einstein received divine revelation, I suppose.)
Maybe dark matter is actually consciousnesses; they get entangled with complex patterns of high and low levels of sodium vs potassium ions.
I bet not. But only because the stabbing randomly around in hypothesis space isn't a very good way to find things.
Drawing analogies where one has no reason to believe that the two processes are actually similar is no better than stabbing randomly in terms of finding something that corresponds to observable states of affairs. If you get lucky, you are better-situated to think about it, so that's nice.
But the advantage over "eh, can't tell for sure what's going on yet, so let's learn a lot more about this absurdly complex system that would be the thing implement consciousness if that's how it works" seems hard to discern.