It is pretty unusual in most parts of the world for landlords to get access to one's credit records. Credit reporting is a pretty US-specific phenomenon, even if you're applying for a bank loan or a credit card.
You usually present proof of earnings and possibly references from previous landlords. And if you get unlucky - well, same as in the US, in many of the nicest markets, you're facing an uphill battle to evict people.
I guess it depends per country. In Germany it has become common that the landlord will require a credit score (called Schufa) plus the things you mentioned (3 months of pay slips, references of balances paid from past landlord).
Strong data protection rules have made it that there is now a credit score report which is only giving you a pass/fail so that landlords don't know too many details.
AFAICT Schufa is not like a US credit score. It's just OK/NOT OK, or a list of "infractions".
Which means if you always paid your stuff on time, a virtual +1 is the same as a +1000, and the visible result will just be "OK" and after a while the entries will age out if it was a "NOT OK"
In the UK you invariably rent through an agent who has access to credit reporting, the cost of which is passed on to both you and the landlord. If you're self employed or a company director then there are a few other things you have to pay for, £45 to look at your balance sheet, for example, which is freely available to anyone else.
I know a few landlords and despite the efforts they take to find the perfect tenant, they all have tales to tell of people who passed all the tests with flying colours but soon turned out to be a costly disaster.
Standard practice in Germany, although the credit system here is a bit better than the US since it works by "demerits" rather than "building credit". Meaning you start out high, and only lose credit if you fail to make payments on a loan.
Also I think landlords can only see a high level summary and final score, not the details of your financial situation.
* A mafioso comes for a chat with the tenant and they move out. This rarely happens.
* The case is presented to court and they'll evict the tenant in about 2 months. This usually happens.
* The tenant has small children and is poor. The owner is fucked as the court won't do anything - the tenants children have a basic human right to a roof over their head. This also rarely happens, but when it does, the damages are huge. My great aunt lost 1-2 years of rent and about 10k in damages due to neglect this way.
Because of this, there are interviews for tenants. Mostly just a chat, but rarely you need to prove you're employed and provide bank statements.
What happens in most cases is that rents go up, because landlords have to factor in this uncertainty. And the debt of the non paying tenants is collectivized.
Rental prices are based on the rental market price and then affect house prices. A landlord deciding they aren't going to make enough for their risk at the market rate and selling doesn't change much as whoever buys either stops renting or is going to rent it out.
You usually present proof of earnings and possibly references from previous landlords. And if you get unlucky - well, same as in the US, in many of the nicest markets, you're facing an uphill battle to evict people.