>They are in no way entitled to see your pay slip

They absolutely do in Germany and Austria. Renting is almost impossible without pay slips from LOCAL employers. Pay slips from your previous EU country don't count. So relocating is a huge bitch.

>Whether or not you can pay rent is entirely your problem (North EU).

It immediately becomes the landlord's problem here when they're legally not allowed to evict you once you stop paying rent. So they're trying to be 110% sure you're the ideal tenant who always pays on time. Especially since for many private landlords the rent you pay them is also their mortgage payment to the bank.

>You have a deposit, typically three months rent, that's typically enough to indicate whether or not you're able to pay rent.

Deposits don't mean you're able to keep paying rent since that deposit might be borrowed money or from illicit activities. Landlords want to see stable employment (well known employer, that you're past probation period, etc), not that you have a lot of random money in your pocket when you sign the contract.

I don't support this status quo, but it is what it is because it's a sellers' market and governments don't want to change that.