If you're asking about international payments between US and EU banks, currently you do that using the SWIFT network (i.e. wires). It's $25-30 a pop. And there are significant regulatory and technical barriers to getting this cost down (see the EU's SEPA program for a regional version, and that's with a bunch of countries that have already normalized their financial regulations).
I assume this is because a number of them use "free, easy transfers between our customers" as a selling point, which would vanish quickly if it were easy to do between anybody. Sometimes it seems like we're even sliding backwards -- for example Chase used to have a fairly nice person-to-person payment system, but they recently locked it down to people with their own Chase account.
Sarah Jeong wrote about her experience with ACH fraud here, where her bank account was emptied when someone found her account and routing numbers: https://motherboard.vice.com/en_us/article/why-i-hate-securi...
It's a pain in the ass, but a long time ago an employer errantly clawed back a full month of payroll direct deposits from me instead of another employee. The bank couldn't/wouldn't help, and the company's payroll was handled by a third party who was not helpful at all.
It's not flawless, but it is insulation against ACH fraud, both electronic and forged checks/e-checks (I've been hit by both before).
It also makes it nearly impossible to use most budgeting softwares out there, aside from battle-tested Excel.
As a sidenote, some financial companies named "forex" are specialized in international payments. I use currenciesdirect.com, they don't take a commission and their exchange rate is within 2% of the Google rate. Most other banks apply a 5-10% spread as a hidden fee.
The secret is, they have a bank account in every country, so it's a local payment in US with no fee, and no fee for their bank transfer between their French bank account and yours.
Can "EFT" an amount from any bank account to any other