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.
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.
Being a French national and not being able to get a mortgage to buy an apartment for my mum is also more than a little frustrating. And that's despite having quite a bit of money saved.
I've rented apartments without credit by showing paycheck stubs and bank balance.
Outside of living off the grid, paying everything in cash, how do you want to have privacy about how you spend your money in this day and age?
Bulk surveillance is a problem as well, but a big topic for another day.
I guess where we differ is that between banks having lousy security, social medias and search giants selling all our data, the cat is already out of the bag when it comes to privacy and won't be put back until law is updated to have teeth, so I see that as a separate problem (which does bother me) that's orthogonal to the 3 companies credit scoring system.
That doesn't mean that it shouldn't be solved, I believe Equifax, Experian and Transunion should be heavily fined for any breach of data especially considering how important the data they have.