I don't agree that it's unfair on tenants to not allow pets. Limiting potential damage and costs is a practical part of the business - a happy tenancy often requires understanding and compromise on both sides.
Renting is very different to owning, with positives and negatives. You can't have it all, as such. Same with owning, too!
Certainly when I rented, I never considered having a pet as I would have been worried about damage/cleaning costs and finding available properties.
I do have sympathy for tenants wanting a pet, but this sympathy has been abused in the past and I've found holding a firm no pets policy has really helped install boundaries and protect properties.
I said yes to a tenant's little girl having a hamster. The next inspection, they had a parrot. The next inspection after that, they had a kitten.
The hamster escaped and bit through trunking, then electrics and the telephone line, the parrot was often let loose in the kitchen and I had to replace kitchen cabinets after the tops were covered and warped in bird poop, and the wee kitten pee'd and pooped throughout the downstairs and the carpets were stinky/stained. It also scratched the carpet at the bottom stairs to bits.
The damage cost to me was well over £1000, but the DPS only (legally) awarded a small fraction of the fees from the deposit.
If I'd had said no to the hamster, they wouldn't have got the bird or kitten and I would have saved a considerable amount of money.
It's not fair for me to pay for damage caused by tenant's pets if legally I cannot be reimbursed those costs.