One of the key phrases I said was "(if you have to make one at all)" -- wavefunction collapse is inherently messy, since the notion of measurement is not well-defined or understood. I would argue that "don't care" is likely a more common interpretation among practicing physicists (of which I am emphatically not!), as this is very much in a realm where general intuition largely does not apply.
Copenhagen is basically an admission that we have no good intuition for why QM behaves the way it does, and wavefunction collapse is merely a way of justifying existing observations within the framework of QM.
IMO all the discussion about how wavefunction collapse doesn't scale to larger ensembles of particles, or the boundary between QM and Newtonian mechanics being ill-defined is noise -- the bridge between the two is statistical mechanics, where classical mechanics only arises from sufficiently large macrostates such that you can aggregate out any quantum mechanical properties. And QM is generally understood to be a toy model in the same way that Newtonian mechanics is a toy model -- it's useful in the realm where we use it, but when you push beyond the limits of that realm, its deficiencies become apparent.
That's why I don't think the proposed experiments to test many-worlds are particularly meaningful (since AFAIK they all seem to involve performing interference on enormous ensembles on the scale of entire humans) -- it's well beyond the limits of where QM is useful (also, I personally don't think we'll ever be able to operate quantum-mechanically at that scale).