Don't know they are not doing this already too but seems you could go asymmetric. The handsets could send to the tower with 64QAM and the tower could use more radiated power to send 256QAM back to the handset.
Phones are no longer symmetric data entities it probably is the case most smart phone users pull down much more than they send now. Of course you can crank the radiated power from the towers up to much or you are just going to start competing with the neighboring cells more. So I don't know how big the gains would be.
Yes you can do some of that but even broadcasting from a tower at higher power levels will not fix issues. Multipath it one issue that will not go away with more power, if you are standing next to a metal building your phone will get two signals the direct one and the signal that bounces off the metal wall at 256QAM the modulation could easily get washed out by the reflected signal. A SNR of 30dB is needed for 256QAM there are many areas that fall short of that requirement.