A few banks also allow to send ACH transfers to third-party accounts that you don't control - for example with USAA that's possible. This still doesn't 100% match how transfers work in Europe (you first need to add the account, then wait 1-2 days, then you can send funds to it), but it's definitely better than "signing a bunch of forms".
I keep hearing this, but out of the many banks I've tried I've never once seen this happen. I just looked at a recent transaction; email shows I initiated it at 9:18am PST on Jan 30 (which could be past the cutoff if it was noon EST), the withdrawal account shows the money deducted on Jan 31, and the deposit account shows it landing on Jan 1--one business day, right? Nah, or at least I'm not informed of them on those days. I don't see them show up for another day or two. When the money does show up in the account, it's often "not available" for another day or two. I'm just one dude who happens to have a few different banks for savings and my wife's account and tries to pay bills on time. This was also a thing when I was pooling money for a mortgage downpayment. I can't imagine running a business.
It frustrates me that for a country that deifies financial markets and capitalism will ignore liquidity like this (even between accounts owned by the same entity). 1 business day (before the cutoff!) still isn't that great. The docs I found about same-day ACH said it was approved in 2015 and only rolled out last year...and it looks like they charge a fee per transaction[1][2]
[1] https://web.nacha.org/system/files/resource/2017-08/Same-Day...
[2] https://content.capitalone.com/TMgmt/images/Same_Day_ACH_%20...
That's very similar to SEPA transactions, with the exception that some European banks support real-time settlements for SEPA. For banks that don't support this yet funds usually arrive on the next business day.
Transfers between the US banking system and the European system are usually slow and expensive as those two systems aren't directly linked to each other. So you your bank needs to send the funds to a correspondent bank which forwards the funds to the final destination. But if you use 3rd party services such as TransferWise those transfers are significantly faster and cheaper. My last transfer from my US bank account to my European account (via TransferWise) arrived on the next business day and cost something like 0.36% on top of the mid-market rate.