Decreased expression of MHC I in tumor cells allows them to dodge recognition by CD8 CTL's. CTL's are big players in the aquired immune system recognition and destruction of viral/tumor cells.
NK's on the other hand are apart of the innate immune response and work via two signals. One of them is MHC I... Normal cells express both signals: the activating signal and then deactivating signal (self MHC I) - the latter being pro survival for the cell. Cells that express the NK activating signal and lack MHC I (the deactivation signal) will get killed by the NK. This does seem contradictory to what occurs with CTLs.
My sense is that CTL evasion provides a long-term survival benefit that outweighs any increased NK response. Confirmation anyone???
As I recall, macrophages don't generally kill tumors via MHC I. Rather, they (along with neutrophils and eosinophils) bind to the Fc region of antibodies that recognize tumor specific antigens (TSA).