Pretty much all cellular communications nowadays uses CDMA of one flavor or another. An important property of CDMA is that any signal that I send to the tower actually causes more noise for the other users in the network. This id called being interference limited. For this reason, there is a ton of effort going into power control, so that reach user sends just enough power to reach the tower but not more. Your cell phone COULD boost it's transmit power to reach the tower, but it would ruin everyone else's connection.
I can imagine that you could rig your cell phone (or another device) to transmit at high power to jam the connection, but the FCC would have something to say about it. If you're caught, I'd expect civil and criminal reprisals...
Without hard proof of such an effect from radio transmissions, your post falls into the bucket of baseless scaremongering. Behavior like this only results in impeding technological progress.
The impact on specific diseases is still in its infancy, and thus shows little results. I doubt any oncologist would have install your proposed solution...
Cell phone companies could put "always on" cell phone repeater in my car, drinking from a large li-ion battery that is charged by the engine, so when my smartphone doesn't have enough punch to reach the cell tower, it has enough power to reach my car's repeater, which has enough power to reach the cell tower. If I could charge the company 0.001 cents every time someone else's phone routes through my repeater, the company could save billions on cell towers. Use the nation's cars as a mobile cell phone network. A Billion dollar idea right there.