Nobody is really expecting large objects to behave differently, but somebody should still check.
From the perspective of a theoretical particle physicist these theories are also awkward because they try to fiddle with non-relativistic quantum mechanics like the Schrodinger equation. But that equation merely arises in the non-relativistic limit of the more fundamental relativistic quantum mechanics, more commonly known as quantum field theory. Therefore, if you want to probe the foundations of quantum theory then quantum field theory seems like a much better place to start.
As an analogy, these attempts sound like a nineteenth-century person trying to understand gravity starting from F = m g h rather than F = - G m1 m2 / r^2.
For these reasons I would not be supportive of significant funding for theoretical or experimental research in these collapse theories.