It's not that you need to be young to do this job, it's that in a lot of areas and systems that pay, benefits and working conditions are such that not very many people can make it a career when spouse, family, mortgage and the like come into the picture and are forced to move on to more viable careers.
In my service however, we have a great many medics who have been in the service for 15 years plus. We have one guy whose seniority date is in 1968. Many of them have shifted to quieter stations or moved into management but they're still around. The main factor leading to so many young medics where I work is the rapid expansion of the service both as the area grows rapidly and since the service was created ten years ago and the area was underserviced by Hospital, Provincial, Private and Volunteer rather than the single Regional service we have now.