Even long before banking became digital, most European countries had an efficient bank transfer system in place in parallel to checks.

Both have their advantages, and I accordingly find it baffling that the US only got one, but not the other, and even more baffling that this has largely survived the transition to digital transfers (consumers usually can't initiate ACH credit transfers to third parties directly).

Meanwhile, most European countries are now left with nothing but a bank transfer system.

This is mostly fine, but the ability to essentially give somebody cash in-person without actually having the cash would come in handy sometimes.

I know checks can bounce, but I always feel a bit uneasy when I tell people "hey I just send you a transfer I promise, it's friday so it'll probably arrive after the weekend, here's the transfer confirmation PDF that I so totally couldn't forge in 10 minutes."

Checks don't achieve that, though. As the payee, I have no way of knowing whether the check will bounce, so to me, it's really roughly as good as a promise that the payer will transfer me the money once they get around to it.

Also, unless you're in an area without Internet connectivity, the payer can these days just initiate a SEPA instant transfer, right?

For Germany, you can get a check secured by the central bank. It is costly, but that check is as good as cash. It cannot bounce.

But it’s really only used for things like real estate auctions where the buyer needs to pay 10% or so on the spot.