If your rental is $2400, and it sits on the market for 2 months, you lost potentially lost $4800. It would take a huge rent increase to justify that.
It's one thing if the software is helping landlords jack up prices to the market rate. It's quite another to convince them to collude against their best interests.
It is a different unit every month though as renters are moving out all the time. This isn't about 1 unit that is empty or not. It is about 100+ units where it can be 89,90, or 91 empty - if the other units that are not rented pay enough higher rent because the empty is not on the market you are better off.
If all units are being rented there is no collusion as the market clearing price is being charged. Collusion requires taking supply off the market in order to raise prices.
It is not possible to raise prices without lowering supply if the seller is already trying to maximize profit. Sure the seller could be undercutting the market but that has nothing to do with collusion. Apartments rent in an auction, each fills for the most anyone will rent it for. In order to raise prices landlords need to increase the competition for each unit.