I'm not sure what insurance is going to accomplish here. Tenants could negotiate it in the contract, but most people are not lawyers who will understand and negotiate the finer details on a contract.
The law is not automatically the best fix for all kinds of bad behaviour, and in many cases it clearly isn't, but I think this is one of those cases where it really is. Dramatically raising rent prices on someone who is already living there, is taking of a situation where the other party cannot simply refuse the offer, because moving every year gets really expensive quick. With many other kind of subscriptions, if the vendor suddenly doubles the price, they're easy to cancel. But not when it's the place where you live. It's taking advantage of a kind of vendor lock-in. A kind of monopolistic abuse.
And it's exactly the kind of thing that many countries do try to protect tenants from.
And no, the problem here is not pent up demand for building. That would be a likely cause when it's the initial rent for a new tenant that's too high. That's a sign there are simply not enough houses and too many potential tenants. But when the initial price is low, the landlord clearly does want to rent it to you. And when they then dramatically raise the rent, they're taking advantage of the power they have over your living situation. Preventing that by law is entirely reasonable.
Individual people would likely not negotiate themselves directly, because they are not lawyers. But they would take contract terms into account when comparing places to rent.
"700 USD per week" vs "800 USD per week and rent increases limited to 7% a year" are relatively straight forward things to compare.
You are right that landlords have a limited monopoly power when people have moved in. (And depending on market conditions tenants also have limited monopsony powers, because it's a bit of a hassle to find a new tenant.)
But those kind of longer term engagements are pretty common in the commercial world. And they are often solved with contracts.
What's keeping people from coming up with those terms themselves?
Note: I am not suggesting that landlords agree to those terms out of the goodness of their heart. They would offer such a ceiling on the increase eg in return for a higher starting rent. They are essentially selling a call option.
If they price the option premium right, they would make money. Just like any other kind of extended waranty you can buy.
The law is not automatically the best fix for all kinds of bad behaviour, and in many cases it clearly isn't, but I think this is one of those cases where it really is. Dramatically raising rent prices on someone who is already living there, is taking of a situation where the other party cannot simply refuse the offer, because moving every year gets really expensive quick. With many other kind of subscriptions, if the vendor suddenly doubles the price, they're easy to cancel. But not when it's the place where you live. It's taking advantage of a kind of vendor lock-in. A kind of monopolistic abuse.
And it's exactly the kind of thing that many countries do try to protect tenants from.
And no, the problem here is not pent up demand for building. That would be a likely cause when it's the initial rent for a new tenant that's too high. That's a sign there are simply not enough houses and too many potential tenants. But when the initial price is low, the landlord clearly does want to rent it to you. And when they then dramatically raise the rent, they're taking advantage of the power they have over your living situation. Preventing that by law is entirely reasonable.