Actually, this discussion of buying vs. banks giving us checks makes my original question even more stupid, because the bank gave us that box for free, and I’m pretty sure I can order another for free any time! Now, my other bank does make me pay for checks (which I think is what made my brain wonder about buying new checks, even though I don‘t have any checks for that account), but they’re actually not nearly as bad as some—almost on par with the online/mail order places, which I have purchased from many years ago before I started paying for everything online.
To answer the questions about why we’d buy:
In the US, not all banks provide free checks. In fact, I’d dare say that most require you to purchase them, or will give you your first book free, then require that you purchase them. To purchase them, you can go through the bank: they will deduct the cost from your account and mail you however many you order; or, you can purchase them from a third party check-seller that usually has all sorts of designs and styles to choose from, often for far cheaper than the bank’s plain ones.