Old Man Andrews Sterling is our best player, he should be playing regardless of what he does (within reason).
He wants to win, Gomez wants to win. Southgate should have turned this into a positive.
I think the timing and handling of it is excellent.
One of the things that has consistently held us back is a lack of squad cohesion with divides based on club allegiances. This has allowed Southgate to show he's not going to accept that kind of shit and try to stamp it now and at a time when not having our best player available shouldn't really matter.
Pandering to a star player, or being over reliant on one, is another thing that's consistently damaged our chances going into big tournaments. This might also help that mindset a little too as it shows that no one player is bigger than the squad etc etc.