Really? On Costco, Target, Best Buy, etc., the overwhelming majority I can see (or filter by) are 4k. The 1080s are actually much rarer than I expected.
(edit: or maybe you meant that most people bought their TVs a while ago and never upgraded?)
Sure, but PIP only on some inputs is confusing and unsatisfying. Why can't you PIP between streaming box A and video game system B?
Probably cost. The increase of including some hardware/software to do this would probably impact the overall sales. Not enough PIP demand.