Physical activity increases lifespan primarily by lowering the likelihood of falling and breaking your hip. If you break your hip, your life expectancy is dramatically reduced. If that's your goal, just train your legs!
That said, I think the most important part of exercising is the mental boost it provides. It's like a healthy drug. There are no negative side effects, and it's highly praised by society.
There's also a lot of reverse causation here. Healthy people don't fall very often and when they do they generally don't break their hips. Falling frequently and suffering broken hips when falling are both general signs of poor systemic health and overall fragility which portend a short remaining lifespan regardless.
It's probably just me but I've had the opposite effect. When exercising I typically can focus less and I'm less productive.
My most productive days are when I just start working on my computer after tea/coffee in the morning and can keep building momentum over the day. Any distractions like exercise break my momentum.
True, however I know a lot of people over 60 who think that walking alone is sufficient. You need to strength train too. Train your abs and at least do body squat variations. Walking is great to lose weight and keep your heart healthy, but not sufficient in itself.
That said, I think the most important part of exercising is the mental boost it provides. It's like a healthy drug. There are no negative side effects, and it's highly praised by society.