Simplify IMMS#startInputUncheckedLocked a bit

This is a follow up CL to our previous CL [1], which made

  InputMethodBindingController

per-user instance.

There must be no behavior change in this CL.

 [1]: Id6e9eca6caaa8edde8c4a405448c31c0ca986509
      2238ecd4

Bug: 325515685
Test: presubmit
Change-Id: I80cb41e8e9f14cb893152d31fb6c86d446e9f884