They could already do that. Nothing was stopping them from forming an oligopoly or landlords association/guild or whatever you want to call it and raising rent in lockstep by 7% each year. The entire point of the 7% cap is to stop that from happening above 7%, because certain hotzones experience that already, not because of a formal agreement, but because the demand outstrips supply by that much and supply can't (or won't) catch up.
However, there's an issue with how you're calculating the market rate: You're assuming that tenants can/will bear that cost indefinitely, so the market rate can be "whatever the landlords want to make it". That won't always be true, not just from landlord defectors who might try to undercut the oligopoly on price, but because the tenants can move elsewhere and effectively remove demand.
> Nothing was stopping them from forming an oligopoly or landlords association/guild or whatever you want to call it and raising rent in lockstep by 7% each year
Well, “Nothing” is an unusual way of referring to the Sherman Anti-Trust Act.
Let me put it more simply, all that rent control does is put a damper on large increases [1], but the rental market will still seek a market price. The only way to do that is to spread the increases to leaner years where the natural rate increase would be lower than the cap. Every landlord would independently conclude the same, no collusion needed.
To undercut that this year would mean being below market price in a future year. The only arbitrage would be between present and future prices. Perhaps some subset of landlords only seek to rent out for the front-end years, so they would have a different calculus, but all that would do is to pull down the average transaction price by a little, according to their size in the market. So if the current price demands a natural increase of 2%, maybe the market will clear at 5% instead of the 7% max, but it remains the case that there will necessarily be years where the clearing price is higher than without rent control.
[1] This is assuming the government "guesses" it right that 7% is the average rate of increase over the long term. If it is below average, then the market gets severely distorted.
I'm saying that game theoretic situation you proposed where every landlord raises their price by a similar amount is exactly what the law is working to limit to a fixed ceiling because the situation you described already exists in enough areas that there's political will to do something to limit the maximum yearly percentage increase.
And the cap was explicitly set to be below the average rates of increase for many areas because the effects of the higher increases in those areas is what the law is explicitly trying to prevent.
Spreading the increase to a leaner year only works if the unit is below the market rate. If the unit is already within 7% or so of market rate, then market won't bear that increase. Instead the tenant will move out to a market rate unit. If the entire city increases in lockstep that means people near the bottom of the market will be literally priced out and either move to another city or resort to sleeping in their cars or become homeless, but everyone else will just downgrade the size of the unit they rent since once the price of the current unit exceeds their ability to pay. At the very top end of the market that will mean units will have decreasing occupancy rates assuming the landlord refuses to compete on price to increase demand and insists on capturing the 7% increase.
However, there's an issue with how you're calculating the market rate: You're assuming that tenants can/will bear that cost indefinitely, so the market rate can be "whatever the landlords want to make it". That won't always be true, not just from landlord defectors who might try to undercut the oligopoly on price, but because the tenants can move elsewhere and effectively remove demand.