There was a link earlier in this thread to a page detailing Target's implementation of CurrentC, and the listed acceptable payment sources were limited to cash, CurrentC, and the Target branded RedCards. I believe once MCX is rolled out, the retailers won't be accepting non-store-branded CCs, but I may be wrong about that. It seems that they wouldn't, though, because one of the stated reasons for developing CurrentC was to bypass the higher CC rates for the lower ACH rates. Maybe those additional store-branded cards will come with lower transaction rates as well.
Either that, or while their store-branded cards are charged the same higher CC rates, they're counting on enough people to use the CurrentC payment to offset them.
But, I have a feeling bypassing those higher CC rates is only a part of reasoning and their main purpose is to gather and keep as much personal information about their customers as possible.