Interestingly, your example is an actual thing we used to have.

In 1996, I picked up the phone on my desk, dialed a 3 digit code, said “I need to fly to Los Angeles on Tuesday morning, returning Wednesday evening”. A couple hours later, an envelope appeared in my inbox with plane tickets, rental car reservation and hotel reservation.

Then every company in the world fired all the secretaries over the course of the next few years to cut costs, and we’ve collectively forgotten that it was ever like that.

Your example is a great example because the secretaries are clearly filling in the gaps, such as

1. How much can you spend on this trip? 2. Is first/business class necessary? 3. Is a layover acceptable if it's cheaper? 3a. Is it better to have a 4am flight nonstop or a 7am flight with a layover? 4. Are there preferred airlines? 5. Are there preferred hotel chains? What's the hotel budget? Do you want to pay extra for a nice view? 6. What kind of car should you rent? Is there equipment you'll be handling?

etc...

This is the kind of stuff that's easy(-ish) to communicate by presenting a list of options to a user through an actual interface. It sucks doing it through voice; think of the old phone systems where you had to go through droning "If you would like to rent an SUV, press 1. If you would like to rent a sedan, press 2. To speak to an operator, press 0."

So no, you never had a voice interface for booking flights; you had a human brain to whom you delegated, which is very different.