Does anyone else live in a place where there isn't a visible "score" for how valuable you are, but rather only a "credit check" for how risky you are, which is performed if you apply for new credit (buying anything with an invoice, getting a credit card, or taking any other kind of loan)? Meaning that if you have a good income and no history of failing payments, you are basically passing the check with flying colors, and will have the same "score" as someone who has had tons of well-served credit before?
This thing where the score as in "risk" and score as in "business opportunity for lenders" is intertwined, and creates weird incentives for consumers, is that only a US thing or do any other countries have something similar?
Credit scores in the US function similarly to this risk assessment you describe, with the caveat that there is no standard way to measure risk without a credit history. In my experience, it does not take very long to establish that baseline, and there are inexpensive vehicles to do so, such as secured credit cards. Small-scale lenders are likely to accept alternative documents like income statements or proof of payment history to qualify. FICO scores, as imperfect as they are, merely simplify the risk assessment process.
Credit scores aren't a score of how valuable you are, they're a score of creditworthiness or how unlikely you are to default on a loan. The largest factors are age of credit and payment history. Utilization is also a factor. Someone who occasionally misses payments and has high utilization is going to be more profitable but higher risk to lend to.