Having bought my first F in '70 while an Army still photographer and used the succession of Fs until '95 as supplied by my rich uncle Sam, I never had the F, F2, or F3 stop working of its own accord. They do stop working if submerged for any length of time or smashed.
I'm still using my original personal Fs. (The reason I bought them was that the government expected me to use a 4X5 for everything but slides and we had one Spotmatic with one lens.) I only recently had one CLA'd because the slow speeds were getting really slow.
The F3 with HP prism is the only F3 I would consider. The older you get the more you appreciate it.
I have had the UD 20mm for more than 40 years. My favorite lens, but big. The 2.8/28mm (.2m min focus) is Nikon's sharpest, best WA. The 2.5/105mm is perfect.
Ai lenses with ears work on F and F2, non-Ai work only in stop-down mode on the F3.
Of my Nikons the F3s get the most use. Never had the motor on the F or F3 fail on its own.
The F will never let you down. Try many screens; find what YOU prefer. Different jobs dictate screen choices.
12 Nikons/14 NIKKORS