To be honest, in Germany even the brick and mortar banks provide transfer services. They will detect and move your automatic payments. You usually fill a form, login to each bank and they send automatic requests to move stuff. Similarly my broker also supports moving accounts for me.

Moreover, especially after the Wirecard scandal, I wouldn't trust any company that doesn't have a banking license. Without a banking license they can nuke my entire account and I will be the only responsible idiot for that.

Btw, the US system is exploitative and decades behind what the worst European countries have. NFC payments became a thing after Apple brought them to the US. Europeans, heck, Middle Eastern countries were already using NFC EMV payments for 5 years by then. The technologically best and most trustworthy banks are usually from Northwestern Europe so look for Nordics and the Netherlands, if you would like to see a modern but not totally exploitative banking looks like.