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.