This is actually quite typical of Tywin, trying to divide and rule. Littlefinger has the title but doesn’t have the power (for some weird worldbuilding reason) to rule the Riverlands de-facto; the Freys have the power (although they’re spreading themselves quite thin) but they don’t have the legal authority to rule the Riverlands.
As a result, everyone remains dependent on the authority of the Lannisters in King’s Landing.