This is perhaps obvious, but flying coach can be good because it’s cheaper than flying in business or first, which means you can take more trips using the same sum of money or number of points or miles.
Frequent flyer miles are wonderful because they make first class much more attainable for the layperson. While a first class international ticket might be 10x the cash price of a coach international ticket, the miles required for a first class redemption might only be 2x that of a coach redemption. But even at 2x, that means that you could take two trips in coach for the price of one trip in first class, so the question should be whether you derive more utility out of visiting an extra destination or traveling to just one destination much more comfortably.
Of course, this is less meaningful if you have more money/points/miles than time, especially since it’s relatively common for people to have full-time jobs that only allow them two weeks to travel per year. But I think for many people, the destination is more important and memorable than the flights, so it makes more sense to use frequent flyer miles to optimize for traveling to more destinations than to optimize the relatively shorter flight experience. And while flying in coach might make the first day at a destination a little rough, I find that I forget about whatever unpleasantries that occur during a flight almost immediately.