Why do Tesla and other manufacturers use AC motors?
I know they could use synchronous permanent magnet motor and run in from DC


This is the problem in your understanding. You cannot feed DC into a motor with no brushes. It will lock up and not spin.

All spinning motors are AC at heart, even brushed DC motors. You need AC (i.e. currents that change direction) in some form at the lowest level to produce a rotating magnetic field to spin. It is just whether you use brushes or electronics to convert the current from your DC power source into the AC the motor needs, or whether you run it off AC directly. Think about what commutation really is, whether with brushes and sliprings or electronics, in any "DC" motor. It's just reversing DC currents to simulate AC.