Wave function collapse is a misnomer. We now know that weak measurements do not collapse the wave function but rather drives the probability amplitudes of the states towards an eigenvalue. For those familiar with linear algebra recall that power iteration of a matrix with a random vector will yield the matrices eigen vector given enough iterations. Collapse is similar to this phenomenon but non deterministic.

My theory: The reason we perceive collapse as irreversible is because the computational complexity of reversing the equations is very high. Especially as the state converges towards an eigenvalue of the measurement operator, it becomes more difficult to reverse. This is similar to how a hash function is reversible in principle but not practice. My two cents.

Many worlds and such are just pseudo religious nonsense.