Flatten SplitscreenPipMixedHandler into DefaultMixedHandler

It was just a thin wrapper and thus unneeded abstraction.
Additionally, the mixed-handler is for general mixing, so
wrapping it in a name for just one combination is confusing.

Bug: 244486556
Test: Tests pass (meaning it still works)
Change-Id: I7a02f803fa421bbec02344d479d1d90ea741e155