How do power banks like the OmniCharge, convert 3.7V to 120VAC?
I briefly read the specs on one of the Omnicharge devices. It tells me it will supply 100W of 120/240VAC. That translates to an input of around 30A @ 3.7V. That is not too unreasonable if they choose their mosfets carefully. If we were talking about 500W, then the losses would start to mount up and you'd generally want to go to a higher DC input voltage.
What we're talking about here is I2R losses - going to higher input voltage means less current thus less loss due to resistance of the wiring, battery internal resistance, mosfet on resistance etc.
Realistically, the whole proposition is a bit dodgy. 100W of AC isn't going to power much apart from your phone charger, your laptop charger and your cordless toothbrush. Running a phone/laptop charger via AC is really stacking up the losses. Maybe there's another use case I haven't considered?