They pay a vastly reduced rent though.
No. Private tenants pay a vastly inflated, unrealistic rent. The more affordable social housing there is, the better it is for everyone, including those who rent privately, as when there isn't such pressure on housing, they will no longer be able to charge extortionate rents.
I have been paying rent on my council house for 15 years (and have had other council houses in the past).
Where I live now there are no mains sewers. No mains gas. No street lights. No school in this village. (Closed down in 1960s, as was the other one in this parish). Nearest police station is 7 miles away. Not even a pavement outside my house.
I pay Band C council tax, along with my neighbours who have a helipad and swimming pool.
My house was built on a corner of a field in the 1940s. Council probably paid off any misinscule mount of £ it cost to build, by, say 1955. Repairs are minimal. The last major refurb? Paid for totally by EU money to deal with slum conditions.
I pay council tax the same as the homeowners here. I get very little for that council tax.
Now that IS unfair.