Some ATCs make me notice that after the landing clearance (even if I am on a downwind leg…) I don’t have to report any further positions. Are they right?
That’s true. Once cleared to land, calling your position is no longer needed. They have you in the sequence. Just follow the plane in front of you. The ‘report positions’ are there in case you are landing at an airport with no ATC.
If the airport is busy you are creating extra steps for the ATC by calling the legs.