On the other side though, EU wire transfers within SEPA cannot cost more than a domestic transfer and overall the domestic fees are insanely cheap, if not free.

In the USA, wire transfers average $10-25 on the outbound. Inbound, domestic wire transfers are often free, but inbound International transfers can run you $15.

This fee structure is why you see Vimeo and Square Cash (and PayPal before those) become so popular.

Unless you already send wires regularly, they'll tell you to go to a branch once you click send.

Not sure what bank you are working with, but that is not my experience (as a US citizen & resident). I have sent both domestic and international wires completely online.

> I have sent both domestic and international wires completely online.

Were these wires to a company that receives lots of similar wires? Do/did you have a history of sending wire transfers? Were any of these wire transfers a significant chunk of your account balance?

All of these things matter. In the US the average person is simply far more likely to be sent to the branch when wiring $10k than in EU.