I don't see any legitimate reasons for upgrades on-board in your examples :
- a passenger arriving late from a connection : if he's been allowed to board the flight (I mean if his check-in hasn't been cancelled because he was late), he still has his assigned seat. If an upgrade occurs in this case, it's an op-up at the gate but not on-board
- a family separated and another passenger that refuses to move seats : I have witnessed such situations many times but I sincerely doubt the family will be upgraded. Simply, everyone stays at his assigned seat and separated if that's what it means. Period
- someone in Premium who wants to sit with their friend down the back : that's rather a downgrade, isnt'it ? Or do you mean that the friend at the back will be upgraded to seat with his friend ?? No way (this has existed I admit, but for many years now, this practice has disappeared and is strictly forbidden).

The only legitimate on-board upgrade is in case of broken seat and no other seat available in the same cabin. And in the illegitimate ones, we have of course the upgrade of colleagues, family and friends...but we all know this