I agree with all of this, the only part I want to push back on is:
"But what's pretty terrible is the attitude of customer service being "you just have to call, sorry"."
I'm pretty confident in saying it's not the CSR who's deciding this - they probably have either limited access or an explicit directive from above that they cannot do x, y, z in email/chat/whatever. In all likelihood they're an underpaid employee of some outsourced subcontractor to the actual company that decides that.
I think we need regulations on this, the same way we need "if you can sign up from a website, you can cancel from a website" laws. If you offer x via a phone call, you can offer x via text chat too.