Paying more than the mortgage is irrelevant, I will never understand why people bring this up.
Of course you should pay more than a mortgage in rent.
When you pay rent you’re paying for a service, for someone else to deal with it when things go wrong, so that when a fence blows down or the boiler breaks all you have to do is let the landlord know. You’re also paying for energy efficiency, knowing that there are regular gas safely checks and you don’t have to pay anything on top to maintain the property.
When you pay a mortgage you are basically just paying back a big loan. All the responsibility of maintenance is yours, you have to find the time and the money to sort out any problems on top of the mortgage payment. You might well live with things being broken that you wouldn’t put up with if you were renting.
Rent and mortgage are two very different things.
Although you might pay a deposit, you will get that back, it’s not money in the landlords pocket ready to pay for any damage left behind by pets, and even if it were there’s no guarantee it would be enough. You really can’t blame landlords for not wanting to accept pets, or children in properties that are unsuitable.