Your example definitely is something that should have been automated and not good use of an administrative assistant's time, but humans are good at navigating unclear processes and organizations.
For example, in one of my internships, it turns out that someone mistyped my address so my paychecks were sent to the wrong building; after a few weeks of that not getting resolved through HR, the administrative assistant took it upon herself to fix it and figured out whom to go yell at to get it resolved within a few days.
They're also good for things where having specialized knowledge of a process that's not done often can be done by someone who does it more often.
For example, when it comes to corporate travel, our company has a self service portal, and every time I need to book business travel I have waste an hour to figure out the right combination of flights and hotels to use, and another hour after returning to enter all of the expenses in the expensing system; I'd much rather send an email like "need to go to office X between Y and Z, no red eye flights" and "here's the receipts from our last trip, we took client W for a business dinner on May nth" and have it all happen.
Someone who does it several times per week would be much more efficient at doing it than me doing it a few times per year. But maybe in a few years we'll get some AI assistant that figures out that I like seat 3A, departures that are not too early, and figures out how to determine the expense types from various receipts.
For expense types I'm told it used to be eaiser. Then some scammers figured out they could send invoices and they would be paid now everyone needs to waste time tracking little expenses because if you don't even more money is wasted.
So there is a trade off which means some of the tedious jobs can't be automated. Though i agree I shouldn't have to separate my hotel room from meals at the hotel.
For example, in one of my internships, it turns out that someone mistyped my address so my paychecks were sent to the wrong building; after a few weeks of that not getting resolved through HR, the administrative assistant took it upon herself to fix it and figured out whom to go yell at to get it resolved within a few days.
They're also good for things where having specialized knowledge of a process that's not done often can be done by someone who does it more often.
For example, when it comes to corporate travel, our company has a self service portal, and every time I need to book business travel I have waste an hour to figure out the right combination of flights and hotels to use, and another hour after returning to enter all of the expenses in the expensing system; I'd much rather send an email like "need to go to office X between Y and Z, no red eye flights" and "here's the receipts from our last trip, we took client W for a business dinner on May nth" and have it all happen.
Someone who does it several times per week would be much more efficient at doing it than me doing it a few times per year. But maybe in a few years we'll get some AI assistant that figures out that I like seat 3A, departures that are not too early, and figures out how to determine the expense types from various receipts.