It's not. Hospital personnel do indeed ask you the same questions repeatedly to make sure they're treating the right person, but online vendors rarely have such high consequences attached to getting this wrong.

I suspect the real answer is that when they finally hand you off to a live human being, that human is sitting in the boiler room of a third-tier contractor on a different continent than the main headquarters of the business, and they have no idea what you're currently looking at on your screen. It's technically possible to do this handoff with a complete picture of how the user got there, but that requires a degree of technical integration most companies don't seem to want to pay for.

To be fair, in my experience they almost always tell explain the reasoning for repeatedly asking this information "for security reasons I must confirm your information again". Maybe I was just lucky with good places and people, but I never had wondered why the heck they need the information they already have on file (or worse, that I have already told them some minutes ago), because from their brief explanations I understand that they have some form and they must type in my data in there for verification.

I am polite but firm most of the time with agents, but I do get chances to talk with people who have the authority to change things. Raising a stink and ‘let me talk to your supervisor’ really can lead to tickets getting forwarded to people who can fix the process or at least give agents training in how to avoid or manage ‘lights on nobody home’ situations.

Lately I have been facing a breakdown in business processes with my local electric utility that first disconnected my electricity because one of my tenants made a mistake. I think they finally understand that I have three services at two houses at one address, but I went through two periods since then of getting no electric bill for months (which I won’t let slide because the last time they stopped billing me I got disconnected.) Getting that fixed involved waiting three hours on hold which got me talking to regulators again. The crew building the new deck at the other house has also deferred work because they have been unable to get through to anyone there who can turn the service off temporarily so they can work near where the wire comes in.

I could see that being really bad... A 'social engineer' could talk support people into helping them hijack an account.

This is a good point. You can definitely verify a user off of context (signed tokens, etc.), but you're probably right that a lot of folks don't do a great job of that!