They don't regulate tenancies in the UK because such regulation has such a deleterious effect on the rentals market.
I don't recall them doing so in New York or Tokyo either.
Actually, they don't regulate the price when you start a lease, but they do have a complaints process for rent rises. Landlords can put the rent up 5% or 10% every year and usually get away with it if the market is good, but none of this nonsense about doubling the rent.
In other words, not every rent contract (or rent rise) gets looked at, but if anyone tries something stupid, they know the tenant is going to run to the rent review board
Landlords (whether they are local or otherwise) are also looking out for any evidence that
a) your company is paying big bonuses
b) your company has good profits for the year
c) you are spending money (e.g. a new car)
and if they see any of the above, in any country, you can expect them to try their luck with a rent increase. That is why two-thirds of the billionaires keep their identities discreet (and only one-third have a profile like Steve Jobs or Richard Branson), they don't want to be charged $100 every time they get in a taxi or buy an ice cream