presumably I have some credit history as I have student loans and various utility accounts, etc, in my name, although I don't have a car or a house.
One of the primary factors in your credit score is how long your oldest account has been open (or the average age of open accounts, which is most affected by the oldest one).
Ideally, everyone should get one credit card at 18, and then use it once every six months just to keep the account from closing. The sooner you do it, the better. This will have a big impact on your rate should you ever want to get a home loan.
Credit scores are just as much about how much money you will make for the loan giver as it is to your risk level.
Credit card companies (and the scoring companies) don't make more income due to you having more accounts, and the number of accounts metric considers closed accounts, not just currently open ones. If they were trying to determine how much money you make them, late payments wouldn't count against you, and they would factor in whether you pay in full every month or carry a balance. There is a lot to be cynical about in the world of capitalism, but credit scores reflect those factors which tend to be correlated with risk of default.
They are looking at averages for the entire population, so if your habits and behaviors don't fit the standard American consumer model, your score may not reflect your true risk, but that doesn't mean its a scam, just that you are an anomaly