It does seem like a weird loophole and charade to have to split money among many banks. Just give businesses a way to store their money without earning interest and with no risk. As far as I know that’s not an option under our banking system
It's neither a loophole nor a charade: it's diversification to reduce exposure to risk. Bank failures are somewhat coordinated, sure. Still, it's much more likely that one bank fails than N>1 banks. Since you are exposed to less risk, your insurer (FDIC) is also exposed to less risk. It makes complete sense for the insurer to incentivize this sort of behavior.
But what it really incentivizes is putting all your money in a too-big-to-fail bank. That's much easier and just as safe as opening a dozen, or hundreds of accounts. And it results in there being 3 banks in the whole country.
There is, in truth, only one “bank” in this country. The Federal Reserve Banks that hold the master ledger for the official US Dollar market. Everything else downstream is basically redundant legacy infrastructure from a time before pervasive broadband network infrastructure.