Demanding a person on the phone use the website on your behalf is a great life hack, I do it all the time. Often they try to turn me away saying "you know you can do this on our website", I just explain that I found it confusing and would like help. If you're polite and pleasant, people will bend over backwards to help you out over the phone.
With "legacy industries" in particular, their websites are usually so busted with short session timeouts/etc that it's worth spending a few minutes on hold to get somebody else to do it.
Sorry, I disagree here. For the specific flow I'm talking about - monthly recurring payments - the UX is about as highly optimized for success as it gets. There are ways to do it via the web, on the phone with a bot, bill pay in your own bank, set it up in-store, in an app, etc.
These people don't want the thing done, they want to talk to someone on the phone. The monthly payment is an excuse to do so. I know, we did the customer research on it.