The base station also tells the phone to back-off. If the TX were running at full power, the battery will die quickly. Leave your phone in a metal, security cubby and your battery will die quickly; no power control and worse-case antenna loading.
Also the highly asymmetric data usage these days. Very little energy on the uplink.
FWIW I design antennas and amplifiers for a living. The only time I'd worry about RF exposure is to the cornea; that is a proven hazard. RF burns are a right of passage for PA designers, and are harmless as it's the outer skin layers.