Its not like you can not cycle without a cell phone, but certainly why would you go without one? Would you go backcountry camping without a phone? It's just a simple safety precaution with almost no negatives. What if you get hit by a car? What if you get 4 flat tires 50 miles from home? Neither of those things are likely to happen but why not have a failsafe plan in place in case of the worst.
Wearing backpacks is not anything that any cyclist wants to do. That's why commuters use panniers instead of backpacks, which are horribly uncomfortable due to oversweating back, and the high center of gravity is not good. Wearing running shoes (or bringing running shoes) is not a measure that 1 out of 1,000,000 cyclists would choose to do. The solution to a broken down bike is NOT running home. You will walk to a bike shop, train, etc or fix your bike so that you can make the ride. You want a very stiff sole for maximum power transfer. You can walk in cycling shoes, but try walking 30 miles back home dragging a limping bike (20 lbs.) and you realize that cyclists need to carry pump, tube, patch kit, tire irons and most everybody brings a wallet with $$ and a cell phone. Cell phones are so small and inexpensive it'd be ludicrous to not bring one out with you. Granted I've used it only once but that time I was stuck in the dark 30 miles from home and I got a ride home.
Cycling is pretty dangerous too. 2 people died on the Texas 150 Mile MS ride and 1 died on the Pittsburgh 150 Mile MS ride. Having a phone is good in case of catastrophic injury. Getting hit by a car is no fun.
Bike safety, maintenance and repair is just a daily non-issue with bikers. Just pack the stuff in your saddle bag, throw the food in your pockets on your back and hit the road.