My dissertation, which I hope to defend in the next month or two, argues that reductionism is generally a good thing, and in particular mind to brain reduction is pretty much the only rationally acceptable option. As a general rule, the arguments against reductionism are terrible, but since my orientation is also anti-realist and pragmatist, there is one which is ordinarily not considered fundamental but which must concern me. Some argue that reductionism carries the danger of distorting funding priorities, of making research into reducible sciences less important and less worthy of support than research into their reduction bases.
Now, there is certainly nothing inherent in the reducibility of A theory to B theory to suggest that B theory is more worthy of research attention, on either the bridge-law model (Oppenheim and Putnam, Nagel) or the identity model (Armstrong, Lewis, Smart, etc). I suggest that the reason that this conclusion seems so natural is that reduction is taken as indicating that the B theory is more fundamental in some metaphysically weighty sense; that the objects of B theory are more real than those of A theory, or perhaps that reducible things are never real, so that the A theory definitely doesn't deal with reality, while B theory might, unless some further reduction base for B is found. But this is scarcely intelligible. Of course, my own view is that talk about things being "real" is nearly always misleading, either code for something else which should be stated clearly instead of coded, or based on metaphysical prejudices which should not concern us. However, even if my anti-realism is rejected, there are further problems. Consider the identity theory; on the identity theory, A theory and B theory are talking about the same objects. That's what makes a theory an "identity" theory. How could one of them be talking about real things and the other unreal things, if they're talking about the same things? How could one be addressing important matters and the other unimportant matters if they have the same subject matter?*
Of course, that reduction should not rationally influence funding does not show it won't; surely plenty of irrational factors influence funding. I confess to having a prejudice, when facing irrationality, to wish to confront and correct it, rather than invent lies (like the irreducibility of theories) to exploit it.
* I think a similar point can be made for bridge-law reduction, though it would be more complicated.