No, I'm not forgetting fundamentals of EMC, but it's good that you did a little thinking so as to attempt to redeem yourself. This response shows signs of life.
If you check again, you will notice that I listed specifically high frequency EMI as a potential problem for all electronics. I listed only one practical example from a specific thread here. Alas you are incorrect again regarding relative EMI of square wave and MSW inverters. The rise/fall times of output waveforms are typically controlled for Square wave and MSW inverters and they do not generally have high frequency EMI worse than sine inverters, as the latter often have switching rates internally that tend to be much faster, and many sine designs are now transformerless. All inverters typically have very strong common mode higher harmonics in the 500K to 50MHz range; they vary dramatically depending on the designer's EMC skills.
Yes, in fact I have designed, built and tested a specialized ultra low EMF/EMI inverter. Low radiated and conducted emissions was the primary design goal. I selected a low frequency design based on the old Trace Engineering SW Sine series, but mine is a 5 step modified sine for 1500 watt continuous with 3500 watt surge load. The extra step allows for low enough THD to keep motors cool and happy, and the low number of transitions per wave allows relatively low losses using semi-linear, slow rise/fall times. It starts and runs 1.5 HP motors (which is was the other design goal) and has measured THD of 8% and 92% power efficiency. It uses two 1100 watt toroidal transformers and also has very low ELF magnetic fields. It was designed with low emissions as the primary design issue and an improved MSW was selected on purpose for that goal. With NO passive filtration on the transformer(s) output, it has no audible emissions via AM radio within 3/4 inch of the output AC line. (Distortions via spectrum analysis are below 10KHz.) I am still working on the prototype; I'm considering variable speed operation and soft starts for solar well pump application; much as Franklin now does on their single phase solar pump controllers. I'm also adding passive ELF filtering of the DC supply side so that 60Hz doesn't show up on my clean DC. Alas, the project has been delayed due to unavoidable home maintenance projects the last couple months. I'm saving up for a high performance spectrum analyzer to more fully tune the design for lower emissions.
To do a full, true sine wave with relatively high efficiency and ultra low EMI would be a hell of a design challenge, much more so than the design I have done so far. I compromised on a 5 step MSW (1st prototype was a 7 step) based on a couple academic papers proposing such an approach for better THD; though to the best of my research no one had actually implemented this before.
So in short, square or MSW inverters are NOT inherently higher EMI, I believe my multistep MSW likely is the lowest EMI of any ever built. (Not externally shielded and filtered.) There are many internal sources of high frequency EMI (500K to 50Mhz) that show up on the output waveform, primarily as common mode emissions. You can easily confirm this via AM radio. Many inverters will wipe out much or all of the AM band within 8 feet of any connected above ground wiring. Variations in good EMC design are far more significant that sine vs MSW or square or internal PWM rate.
I have some videos showing the 1st prototype design and some testing with an air compressor motor for anyone who is actually interested. It is non-edited and is only semi-technical for a very smart but non-EE friend.
I have also worked on a few projects adding passive filtration to existing inverter systems. This is problematic as most facility type, high performance filter have fairly high levels of capacitance to earth. For many inverter designs, including Magnum's and mine, reactive loads drain the batteries just as well as linear loads. I've worked with Magnum and Genisco engineers to come up with a specialized high performance filter that only draws 15 watts 24/7. Many facility filters draw 100 watts or more, which is hell on a smaller off grid power system.
I don't typically talk about my electronics projects here because it is not the emphasis of this forum. We do have a couple other outstanding EEs here doing professional level designs for embedded MCU controllers. I'm really a EE/CS type but have taken graduate training in EMC 27 years ago and do advanced "hobbyist" level designs.