The US system has issues but it's less broken than every other countries I've lived in.
The idea that everyone is forced to create a public profile so you have the option of getting a mortgage sucks. You have no right to a mortgage at other's expense. If you want folks to trust you, get a co-signer, put down roots and stay a while.
Without a credit score that follows simple algorithmic rules, how do you want to prevent this from happening? A credit score that has rules that people know in advance may be gameable but it also creates fairness by making it easy for everyone to know what to do to get a decent score.
Now, the fact is that the credit score could be managed by government agencies (although honestly, I'm not sure any government is much better in term of data security), there could be stricter fines in case of data breach (that sounds like a good idea), but those are implementation details.
That said, I'd agree that both of our plans could be implemented a lot better.
It doesn't matter what it "should be" proof of or what a reasonable person could infer from this income or documentation of it. If you don't have a CDI, which even many full-time employed people don't, you're in a hard spot.