Yes, Rod1, I do, and so did my instructors and examiner for my PPL. Maybe they were responsible for the anality.
All you do is glance at your watch (or the clock which by law you carry in the aircraft) as you rotate, make a mental note, then write it down when you have a second. I always say it out loud which has the benefit that if I have a passenger I can ask him/her if I forget...
1...2...3... Ts & Ps in the green... airspeed active... 55 knots: rotate ... airborne time 35... FERAF check... 'G-ABCD airborne, to approach'...
Easy to fit in, as far as I can see, unless you are in a jet fighter. On touchdown I note the time as I roll off the runway onto the taxiway.
Incidentally as I think has been mentioned the interest in takeoff/touchdown times is that the tech log requires these for calculating maintenance. Plus knowing the takeoff time enables you to work out your ETA for the first waypoint, unless you have the luxury of climbing into the overhead to set course.
Tim