not quite 12" but the biggest element on mine would probably be great with your skillet (if its the right metal)

That’s one of my biggest objections - too many cheap ones with tiny coils. When I got mine, I ended up spending double what I planned, mostly so I could get useful sized coils

And this being the US where induction is rare and expensive , I had to get a double oven and and “smart” features in order to get larger coils

Consider one of those where you can combine the burners/zones

Omg yes. I'd been wanting to try one out for a long time. My friend got one. Stayed over and tried to make my specialty giant pancakes. Sorely disappointed with the useless results. Now I just bring my waffle iron instead.

i had one (a couple decades ago) that the large burner had two zones: both the ring and the center of the ring could be activated independently. it's been a hot minute so i don't remember exactly how it worked.

and i need a 14 inch skillet for my good pastas

Just looked them up lately; there are all kinds of forms and sizes in mobile or built-in.