Unless you have money to throw away I can’t imagine not checking the details and comparing prices. Hell, even if you do have money to throw away you still want to double check everything just before the last purchase decision. Is it going to the right city? Is it at a reasonable hour? Is baggage included or purchased? Etc
The most useful feature for me is google's price/date grid. For personal travel, I'm flexible with dates, so I always use that to just find when flights are cheap. For work, I try to find the best price, but I'm not super picky since the company is paying for it.
I feel like the travel site UIs do a good job of summarizing all the info and putting it in front of you.
Do you want the agent to book it for you? Or just find it?
Google flights is great and I use it every time I want to fly, but it's very rare that you can purchase the actual flight on google flights too.
There's not a ton of money in skimming commissions off of flights (probably < 1%), but there is if you can attach a hotel booking to it (upwards of 10%), so if you can become the preferred vendor for a business traveler, there's money to be made.
It's funny how many AI tool demos have used flight booking as an example task. I always groan at that. I just don't think that will be the way most people book flights. Maybe the 1%ers or less. Are you you currently doing this?