Somewhere in the archives is my test on small vs big inverters for amps draw in standby and when running a TV. It turned out that there was no advantage in having the small inverter.
The big inverter on short fat wires had less voltage drop and the small inverter actually pulled more amps to run the same TV on its long skinny wires as typical of a small inverter installation.
Standby draw with either was trivial. However, it is not trivial when the big inverter is part of an inverter/charger. Those things have a 12v demand just to fire it up and keep it running with all its fancy features that a simple big inverter does not have.
So be careful when saying "2000w inverter" that you are talking about an inverter or an inverter/charger.
As mentioned, we leave the 2000w PSW inverter on the whole time and the draw from that is trivial (as seen.not seen on the Trimetric) We do turn off the loads on the inverter when not in use, such as the TV by turning off the power bar the Tv is plugged into. The microwave display stays on (also trivial) and even a 120v clock radio (trivial). It is just so handy to have the outlets always live and not have to remember to turn on the inverter before doing somnething that needs it.
If your RV is not set up (or cannot be set up) that way or your choice of RV lifestyle is to enjoy going without some conveniences while camping, that's fine too.