And yet their starting Corner didn't play in the Super Bowl because of something. Apparently, even with the iron fist of the Patriot way, players occasionally make waves. It that players name isn't Brady, then that player sits and/or is gone.
Assuming all the reporting/rumors of the issues with both Landry and Ajayi were more or less true, Gase had two choices: get them onboard fast or get rid of them, otherwise he shows his throat and every player will see if and know it. From everything reported, the team tried. If the coach is ever going to control the locker room, they can't dawdle, they have to be decisive.
Total speculation, but given the modern "culture", I can't imagine that current Dolphins players are looking at the Landry situation as something that will influence them to get in line. Let's assume that Landry truly didn't put in the effort required to learn the offense (I don't buy it, personally). Here's a guy who didn't put in the extra effort...yet he was to go-to guy in the offense for four years.
He gave 100% on the field, didn't hold out when many expected he would, and didn't really make waves about his contract status until the end. He never missed a game. Any player looking at that will take away that Landry had to go somewhere else to get paid. They won't say "I need to toe the line and then I'll get paid".
I don't think dumping Ajayi and Landry would in any way be viewed as a threat to anyone on the Dolphins roster. Ajayi just won a Super Bowl. And Landry is going to get paid, just not by the Dolphins. If anything, the remaining players on the roster will just think more negatively of guys like Gase, Grier, Tannenbaum, and Ross. The Dolphins dumped guys that helped them win games and got nothing in return.