Yeah, that's the other thing that's not mentioned. There's no indication that Sakho was going to keep his spot without any of the transgressions.
Lovren looked like one of the most transformed players under Klopp and Matip was always going to get a chance.
I'm late to the party on the Sakho-fest, but I think the key thing that's missing in all of this is the fact that he isn't without error on the pitch either. Injuries, fitness and form aren't all his fault, but he's had a bit of a stop start career for the last 3 seasons.
He played decently down the stretch last year, but he isn't what exactly fits in how Klopp wants to play. He's not always clear on the ball and he doesn't do what Klopp wants. Whether by Rodgers plan or not, he was looking to make longer passes, rather than some of the quick, feed it up to the central midfield and be an outlet. He's also not always without a gaffe or two when coming out to cover for the backs being so far up. But the trouble I see is that over his track record here, he just couldn't stay fit. He's been in and out of the lineup with injuries, form issues and all the rest. I think Klopp desires consistency more than anything else. He wants to trot out the same back 4 week after week if he can help it.
I think Klopp went with the pair he feels most comfortable with, who fit what he wants to do, and who look like they can stay fit. I mean, the question is going to be is Sakho one of the best two central defenders at this club right now? I think possibly, but not in how Klopp wants to play and that's the key point. I think Matip plays better on the ball and moving into the midfield, and plays better on the right. Lovren has made the left part of it his own, is more steady, and so far this season and last with Klopp looks like a top defender.
Now, I think you combine the fact that he did something dumb and got sent home from a tour, he criticized the manager, along with his problems staying on the pitch and fitting the system, and it makes sense.
I think the loan move was as much a "go get right, prove you can stay on the pitch all season" and his not taking it along with criticizing the manager signed his fate. It certainly helps that Liverpool are playing well.