Besides not being aesthetically pleasing, what’s the downside of strictly using countertop induction cooktops, both commercial and household varieties, as my burners? If I go for the individual cooktops, I could easily replace them individually if they break or if technology or features improve, plus I can put them away for when I need more countertop space. I do use my current built in cooktop as “counter space” during gatherings, but I’m always leery of doing this for safety reasons.
Edit: There’s a wonderful community being built here. Thank you all for you responses and for the great thinking points. While I’m not entirely sure of which direction I’ll go as far as countertop vs built-in, I’m definitely sure I’ll be using induction.
A substantial proportion of the heat from burning gas on a stovetop in the usual manner does not heat the content of the pot, so the difference in thermal efficiency between electric and direct gas heating may not be as large as you might expect. This factor could probably be improved with different stove designs though (cheap burners do a worse job of putting the heat where it does the most work).
Additionally, gas ranges impact indoor air quality a lot more than electric stovetops, and gas delivery to homes leaks into the atmosphere a fair amount of gas with high greenhouse potential (I work for a gas pipeline company on leak tracking software) so there are other tradeoffs that one should consider beyond just thermal efficiency.
I don’t think there’s a one-size-fits-all answer here, both are good options for different situations.