I think you are facing the same delema I did a few years ago when installing my PSW inverter/charger.
Removing the cheap & nasty converter/charger & throwing that as far as I could was the easy part. I am pretty sure I could have done the same with the transfer switch since the documentation on the inverter charger did talk about automatic sensing of 120AC.
However, not being 100% sure, I left the ATS in & ran a shunt, as instructed, right to the 120VAC panel.
My 2000W PSW inverter charger is plenty big enough to handle most anything requiring 120VAC however the battery bank is not. The drill when drycamping is to turn circuit breakers for the microwave, the fridge & the heaters OFF so that they cannot be inadvertently used & rapidly kill the battery bank.
