It is his contention that anyone over 50 should not be doing night shifts as part of a regular rotating shift pattern as it is injurious to your health.
I think your GP is basically correct.
Unfortunately, ATC (as with many other H24 professions and jobs) requires 24/7 shift working and so this is an unrealistic aspiration.
That said, there's absolutely no doubt that recovery time increases beyond age 40 and that beyond age 50 it's debateable whether someone ever fully recovers from night working unless they take leave or some other significantly longer break between their shift cycles.
The one advantage that ATC has over most other night shift professions (particularly the medical professions) is "SRATCOH" (mandated in the UK since 1989) or similar duty time restrictions where these are imposed by the State regulator, and the fact that the duty times and rest periods are both prescribed and (in all responsible employers' ATC units) strictly applied. The best H24 ATC shift cycles move backwards from mornings through afternoons to nights - this has been determined as being the least onerous on and most easily accommodated by, the body's circadium rhythm.
That said - and despite the various social advantages of having time off during the 'day' or 'week' - the jury's probably still out as regards the long-term impact on people's health of working regular night shifts over a 30 to 40-year ATC career, simply because you'd need to study people who began this regime in the 1960s and 1970s and I'm not sure it's being done/has yet been done; and other aspects of the individual's lifestyle would also need to be taken into account.
Be interesting to see the data and conclusions, though...