Most of the issues with "international banking" are infact just issues with North American banks.
I can transfer large sums of money around Europe and it will arrive in few days at the very latest. Within the same country transfers mostly arrive the same day (often it's under 1 hour), and sometimes that happens internationally too. Oh and I don't need to pay anything for that.
A few years ago I was working in the Middle East, and before I moved back I transferred my savings from there (~€50k) back to Europe without any questions from either bank. I just did the transfer online, and it arrived in a few days.
Now I'm working for a US company, and it took them a few weeks to setup paying me with their bank. It usually takes at least a week from when they tell the bank to pay me, until I receive the money in my account - to a USD account also in the US.