Of course the polarizations need to be aligned. Fortunately, aligning the antennas in one polarization is a lot simpler than shifting the phase of the multiple Tx waveforms...
The problem with your proposal is much worse. Do you know how antenna array beam forming and beam steering works? You use destructive interference at the beam angles where you want little/no power, and constructive interference where you want the most power. But there is no magic going on here -- you still are transmitting full power out of all of the antennas in the array, and losing all of the power at the angles where you are using destructive interference to cancel the Tx waveform.
You do get some addition of the power in the main lobe(s), but you still are wasting all of the power at the angles where you are generating destructive interference. It's not like the power at those angles somehow magically gets transferred to the angles where you have constructive interference.
Antenna arrays are not about generating more power. They are about sacrificing power in order to generate a Tx power pattern that is more focused.
https://en.wikipedia.org/wiki/Antenna_array
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