Rent control distorts the market; endless case studies and research is available to show how it creates a worse market for tenants, and we have exactly that situation unfolding right now.
Rent control however is politically popular and is relatively easy to implement; so instead of long term housing solutions we get short term, populist policy.
Tenure isn't a major issue, a good quality tenant paying the rent on the dot and keeping the property clean will have as long a tenure for as long as the owner remains in business.
When there is plenty of supply tenants will simply vote with their feet; owners who don't keep their property in good repair will have voids/non-payment.
Rent controls, for all that it is self-defeating exercise, won't put me out of business.
BTL finance rates won't put me out of business.
CGT, since it arises on sale, won't put me out of business.
But a non-rent paying overholding tenant, who likely will trash the property and will take c. 2 years to remove will put me out of business.
That in my view is the no. 1 reason property owners are ceasing to rent out their properties, in spite of the profits to be made.
Larger entities can subsume the losses into new rents (much as supermarkets make allowances for 'shrinkage' aka shoplifting); smaller non-corporate owners cannot.