Classical QM (Copenhagen, if I'm not mistaken) does have that problem. The collapse is indeed an additional hypothesis done on the part of the wavefunction the math already says we cannot observe. As always, unfalsifiable additional hypotheses are bad.

I can't speak for De Broglie-Bohm, but it would seem that theory also have a similar strike against it: the math is more complex than the equations QM physicists are familiar with. It's just not the simplest theory that fits the observation.

The obvious alternative is to just stick to the math. Problem is, the simplest math that explains our observations implies a universe that forks all the time. For some reason, possibly the intuition of a unique universe, many people cannot accept that.