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A 3 phase transformer doesn’t have a neutral full stop. And as it’s centre tap, each circuit is a pair of phases (rather than a line and neutral pair), each phase being 63.5V line to earth, which then gives 110v phase-phase. The 8 or so circuits per transformer are split evenly between the phases.
There might be losses, but they’re almost always powered by generators and the loads are relatively small compared to permanent installations. I don’t think it’d be cost effective or realistic to try and do PF correction when the loads are changing so often, and when the installation isn’t even permanent.
But I do love a phasor diagram (not that I’ve ever used one in anger).
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Yes, the 110V side of the transformer does but other side of the supply is still at 230V per phase and has a neutral .
If you are using diesel generators then the motor is balanced and you have little choice to use earth as neutral but I've seen generators literally jump when their load side isn't balanced.
This was at outdoor gigs when all the PAR cans were turned on suddenly but it is an issue.
Power Factor correction is more due to capacitor loads than pure reactive loading.
Not sure about not needing a neutral. Balanced loads such as motors don't need neutrals as there is no return current. Site transformers (presumably 110V) aren't going to be balanced across the three phases as each phase has a different load.
It's all about Phasor Diagrams.