Our design uses the sdio/mmc driver also to talk to an on-board eMMC, which is where we store all our code and data.
I have no CPU load problem when accessing the eMMC, even if I try to continuously read or write large amounts of data.
Furthermore, I would have hoped that given that we are using a "supported configuation", I wouldn't have to go and talk to NXP myself, but rather Murata/Cypress/NXP would work among themselves to solve this kind of issue.
Have you tried to reproduce my observations on a system at your end (ie: running iperf3 or similar over WiFi and looking at CPU) ? What transfer speed do you observe ? and what CPU load coming from the driver ?