fwiw, and ymmv, and all that said first
most all motors, and things that use transformers and relay coils like pure sine wave,
if you power them with modified sine, they will run hotter than they would otherwise on pure sine
and if you feed them with square wave, they will run much hotter
having said that, most appliances seem to tolerate the added heat from what i can tell, but
i would expect any appliance that is marginally engineered to suffer some longevity if not provided with pure sine wave power.
having read on here and various other forums relating to offgrid life, folks get very anal about a few milliamps here and there
but pay no mind to the inverter that they use, mainly because the advertised efficiency of a modified sine/square wave inverter
is usually quite high and in some cases equal too or surpassing the pure sine wave inverter, but
folks don't consider what the added heat represents in the motor or transformer loads, that heat relates to added losses
it takes power to make heat.
the thing is, a pure sine wave inverter is likely more efficient overall powering a specific motor load even if it is listed at 90% vs
a modified sine wave that might be listed at 92-93%, the added efficiency is eaten up as heating in the motor load, leaving the overall
efficiency likely much lower than the pure sine inverter listed efficiency.
to me the better discussion might include an analysis of this phenomenon, where folks get all knotted up chasing down a few tenths of an amp
and then burn several extra amps making heat with a modified sine inverter driving a motor load like a refrigerator?
i suspect that there is much more to be said for buying the pure sine wave if possible to start with, the appliances "might" last longer, and the system overall efficiency will likely be higher as well.
over time, maybe not a very long time either, the added cost might quickly pay off?
btw, the only things i have heard of damaged by modified sine and especially square wave inverters are smart chargers for portable tools and
some cellphone chargers. i have seen a few of each burnt up using modified sine inverters.
bob g