Converting between different grid frequencies would need a rectifier/inverter or rotary converter - and one that can handle high power (1200W+ sustained) as well. That's quite a bit of equipment to run just a microwave...
They do, but unfortunately it seems like household products that the global manufacturers offer are very different region to region. I guess the Americas and Asia get the high-end microwave ovens... (but they're also quite different, I'm sure.)
A local appliance dealer who I have come to know on a personal level turned me on to the LG and special-ordered it for me. I had originally asked him about Panasonic inverter microwaves but he dissuaded me saying that the Panasonic ovens suffered from reliability problems.
The inverter cooking is fantastic and makes the oven a lot more useful for serious cooking. I will use 20-40% power for re-heating foods over a longer time and the results are that there are none of the weird molten-hot and still-cold pockets of food. Pre-packaged foods whose directions are, say, "heat for 3 minutes," I will instead heat for 5-6 minutes at 40-50% power and the results are considerably more consistent. Plus, I have found that I can get sous vide-like results at low and long settings. For example, I have discovered that heating a filet mignon cut gently at 10-20%, and periodically halting cooking for a minute to let heat distribute evenly through the cut, and then continuing slowly until it temps at 115°F, and then searing on rocket-hot cast iron produces great results. Better than sous vide, at least for beef tenderloin.
I know I will never go with a non-inverter microwave again as it turns a blunt instrument into a device capable of truly nuanced cooking. If something is going to tie-up counter space, it had better be worth it and the LG is worth it.
Yes, it is a non-microwave "combi oven" convection/steam with precise temperature and humidity control. The breakthrough here is price as traditional professional combi ovens are incredibly expensive. Electrolux makes a small countertop model for about $2k but it does not review very well. Gaggenau offers a consumer built-in that requires plumbing for water supply at about $8k. The gold standard are the Rational commercial combi-ovens which start at about $10k and go up sharply from there.
In roughly the 140° to 250°F range, the combi ovens are super precise unlike anything else. Nathan Mhyrvold in his tome "Modernist Cuisine" says, (roughly), that the combi oven the single most useful device in a kitchen.
For lower temps, sous vide is more precise but, overall, the combi is more versatile.
Anova, along with Sansaire, was one of the first to introduce affordable sous vide circulators to the market so I have high hopes for their $700 combi.
As for a microwave with a user-visible humidity sensor, I don't know of one but I haven't looked.
Edit: Looks like units capable of dealing with these kinds of power specs run for around $2300 USD, e.g. http://www.gohz.com/2kva-frequency-converter