My DP is 70 this year. You wouldn't know it looking at him.
He cycle toured in his teens and 20's. Started marathon running in his mid 20's - mid 30's. Got into bike (mountain bike, cyclo cross and road) racing in his 40's. Took various national titles. He had a break from racing in his early 50's, but kept cycling and running. He did some marathon length fell races in his early 60's. A skiing injury and then later cycling crash stopped him running. The injuries prompted him to start yoga (which he still does). He stopped racing soon after our son was born. He's continued to cycle. He's just got back from an epic cycle tour - 1,000 miles over 2.5 weeks.
He has no mobility or health issues. He's incredibly fit. He continues to mountain bike too. He's a machine. He has no issues tearing after our very active son. We do lots of family walks, backpacking and cycling trips. Basically the man is a product of a healthy active lifestyle!
I'm extremely fit too (I also race). I'm in my 40's. I'd never give up exercise. I've had periods of illness and injury where I've had to take a pause to recover. But I've always got back and built my fitness back up.
I know plenty of women and men racing in their 50's, 60's and 70's. So it's kind of normalised in my head that physical activity and pushing yourself is a normal part of daily life.
Through my job I come into contact with numerous people (my clients) who are not healthy and don't do any physical activity. They suffer poor mobility, poor mental health or general poor physical health (eg with chronic conditions). Many are my age and younger. That encourages me to keep doing what I'm doing. I'm not saying that lack of exercise leads to these issues. However, I'm well aware of the benefits of being physically active - the research is there! Likewise I try to maintain a more generic healthy lifestyle - minimal booze, plenty of sleep, good diet etc. My DP is the same.
Good physical health in older age isn't just about physical activity - but also about a general healthy lifestyle. It's a holistic thing.