I wouldn't for any personal international trips, honestly. With the current air network, you can generally find a route that takes you in when you want it to (more or less), and that first day is already so disorienting that I don't think adding a few hours to it even if you can't find such a route is going to really affect the vacation as a whole that much.
Business is a different story since I wouldn't be paying directly and those trips are generally more fast paced and require you to be at 100% soon after getting off the plane. Those extra hours could help you finish preparing for a presentation or something.
Longest flight is currently 17 hours, 40 minutes assuming concord speeds that would save over 10 hours and again on the way back. That's just short of a full day less flight time round trip.
Granted that's the outlier, but nothing says these aircraft need be limited to concord speeds either.
Business is a different story since I wouldn't be paying directly and those trips are generally more fast paced and require you to be at 100% soon after getting off the plane. Those extra hours could help you finish preparing for a presentation or something.