Why not focus both body and mind? Watching Discovery Channel on a treadmill, jog around while listening to books on tape or language tapes, lifting weights while reading or using the computer, wearing leg weights or arm weights while moving about your time at home, there's all sorts of ways to multitask it.
Being in shape isn't just about aesthetics, come on now. Being out of shape means you couldn't even flee a dangerous situation effectively, let alone defend yourself from it. It allows for ease in mobility instead of being clumsy or weak. It gives greater stores of energy even for stationary tasks instead of feeling drained all the time, and makes for more restful sleep.
"The body is nothing but a vehicle for the mind", the mind is a part of your body, and how you treat your body affects your mind.
I'm not talking about what you "have to do" I'm talking about a tried and true method that has been proven to work for thousands of years. To the point that it's not even about (more recent)higher social matters but of (very old and heavily programmed) basic primal animalistic nature.
Well, I don't want to live in a society of animals. I belive Humanity can become more civil and understanding of eachother as a society and use fair policy with logic and dialogue to solve disagreements. We can do that with the internet. We as a society can unite.
P.S. I skip every other stair AND run up the stairs everytime I go upstairs to my room. I'm fast enough and I have enough dexterity to ninja my way to safety. I don't need muscle. 
Excellent point, if the body is not properly regulated through the right amount of energy expendenture then it is likely to fuck up the neurochemicals that balance your emotions and regulate the way you think. Simply from a neuroscience standpoint, excersize is huge.
I'm sorry that I've gotta break the news to you... but um... you are an animal... of a more evolved species perhaps but an animal none the less. And as nice as it would be for the world to be a beautiful happy place full of butterflys and rainbows... that's just not how it is, it's an ugly violent place where the strong, smart, and the resiliant thrive and the weak are used as pawns.
As for your running up stairs... I can ruck 12 miles with a 50 lb ruck on my back in under 3 hours. I can run 2 miles in under 13 minutes... and I have done marathons with decent times also... If you had someone like me coming after you being able to make it up the stairs probably wouldn't be enough for you. ;)
Jay has a point, exercise is important physically, emotionally and mentally, however pure strength and stamina can be very important when you need to defend yourself or even more importantly your children. My friends laugh at me, but in the event of total economic or social collapse - I want to be as fit and strong as possible!!
edit: like Turncoat pointed out, some people are just plain scary and dangerous!