FIFY
That ended 20 years ago, maybe longer.
No, it's still possible.
As a frequent flyer, I can't be extravagant. My company works through a third-party travel booking service and there are definitely limits on what you can and can't do. In order to go over the limits it catches the eye of people several levels above in ways you generally want to avoid lol...
That said, there are still ways to work around it.
The first is to align your own frequent flyer programs to the company's "preferred" airlines. In my case that's American and Southwest. That was convenient because I was already primarily flying American. But when I go to Denver, and the only real options are Southwest, United, and Frontier, I try to ALWAYS make my routing on Southwest rather than diluting my points from those trips between 3 airlines.
The second is flexible routing. I prefer to fly out of Orange County. When I fly routes that Southwest doesn't favor, I prefer to fly American. If I can't find a routing on my preferred airline that's within the guidelines/limits of the company, I'll drive up to LAX or down to San Diego for a flight. Sometimes that works out in my favor because I can't get a direct out of Orange County but can from LAX/SAN to certain cities, so the extra drive time is somewhat alleviated by the shorter flight/layover time. That's what I did for my trip to Austin a couple months ago. And it had the benefit that if I'd flown from Orange County, due to layovers and flight times I probably would have been forced to extend to a 2-night trip instead of an overnight.
International is harder, but I haven't had to fly international for business since 2015, so I haven't had to worry about it.
It takes a little work and a little flexibility, but you can still align your flights for maximum personal benefit re: points/miles.