Using 110V instead of 220V means 4x the current , so a high power appliance must be much heavier duty, needs to be installed by an electrician, etc …

The USA uses 220V for appliances like stoves.

Europe often uses 3 phase 220V or 1 phase 380V for heavy loads like stoves.

That's not quite right. In Europe three phase wiring is delivered via a 5 core wire: 3 phases, neutral and earth (ground). You can take any phase wire, and the voltage between that and neutral will be 230V. For higher power devices, the voltage between any two phases will be 400V.

My induction hob can be connected to 1 phase or 3 phase power, there's a dip switch on the back to switch it over. I'd imagine inside it changes the voltage and frequency to something completely different depending on what power level you set the burner to, so the actual supply voltage isn't that important.

In the US, most people are buying a range (freestanding stove+oven), while I understand in Europe people are buying cooktops (stove only)

I haven't been in houses in all European countries, but I've seen both. I think a range is cheaper (one appliance, one electrical connection), so you find it in cheaper apartments, cheap rentals etc. It might also be the only reasonable option if the kitchen is small.

A separate oven and hob usually means the oven isn't at knee height, which is much nicer. Decent apartments and houses in Europe have this, but so does my relative's million dollar house in the US.

Yes, I have one of these $50 portable cooktops and it works OK but still takes forever to boil water. The expensive ones are actually as good as gas and I was pricing out the freestanding stove+oven, thanks for backing me up xD