How is that collective bargaining when your neighbors have different landlords?
All you're suggesting is to stop paying rent, which anybody can do on their own, with the usual consequences of your credit getting ruined and then the landlord serves you an eviction notice and changes the locks.
Consider the economics of what you're suggesting. Your unit costs $800k when it should cost $200k because of artificial scarcity (zoning), so then the landlord has to pay $800k for it and charge rents high enough to pay back that loan. The way you fix that is by getting the cost of the unit back down to where it should be, i.e. building more units to alleviate the scarcity.
Demanding that the landlords charge less without reducing what they have to pay for the building doesn't work, because then who is going to sink $800k to build a new rental unit? Who is going to keep renting out their existing units at a loss instead of turning them into condos or similar? Which then makes the scarcity of rental units worse and causes rents to go up.
You can't solve a supply problem by bargaining with someone the law still effectively prohibits from increasing supply.