I've always thought the US system was super weird and backwards forcing debt on people. We don't have credit cards from every big chain and don't get harassed into signing up for cards in the mall, it's just not a thing.
We have the same safeguards you have, but we prove it with sensible spending instead of getting debt just to prove that we can pay it in time.
In the US, the loan originators look at year-end tax forms or recent pay stubs to verify income. They look at credit reports from e.g. Experian to verify defaults and other debt information.
This is all open data and can be verified with just a phone call to the tax office and debt authority. Some private aggregators exist for convenience but they're regulated in what they're allowed to share and for how long.
The private companies are also required to notify me anytime someone checks my score, the government agencies aren't.
It's been years since I had my mortgage approved but I vaguely recall the process being very similar.