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.
Yes, they do offer transfer services. But do you trust their services to be flawless?
Like I mentioned, I've dealt with their brokerage-arms, and it was a disaster. Numbers being wrong between two large banks, the transfer taking _months_, and nobody knowing anything and everybody shrugging their shoulders and going "maybe call the other guys again?"
They have no incentive to make that seamless (in fact, they have every incentive to not make it seamless), and it isn't.
The same isn't true with your phone number. Once you've moved, it just works. You never have to tell anyone you're switching providers. The old provider is out of the picture and you no longer need to rely on their good will after your business relationship ends.
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.