Vintage or spring for one of the newish companies making polished pans (i.e., not lodge). Field, Lancaster, Yeti (acquired a company called Butter Pat).

Not scratching is not a guarantee, that's about care with use.

I have a deep Wagner skillet that while not perfectly flat on bottom, performs wonderfully on induction.

Sand casting has the possibility of sand grain inclusion in the cast iron surface. Perhaps polishing reduces this risk substantially. Ground machine tool surfaces seem to be free of such inclusions, so it behooves the pan maker to grind off enough base to assure freedom from grit.

Get a silpat.

Staub works on induction. I love the dutch ovens I have. The bottom is glazed so no scratching.

Cast iron with cool touch handles isn't a thing I've ever seen.

Is there an issue with cast iron skillets on induction where you have to be very careful that the pan isn’t larger than the induction coil?

I hear cast iron is poor at heat transfer. So, it will have hot areas directly under the coil surface, but the outer edges will not be as hot. Meat in the middle of the pan will be browned, but the meat in outer edges will still be pink and raw.

Perhaps, if you put a 12" skillet on a 6" hob. But I think the same would be true if you mismatched gas/electric burners with oversized cookware.

Apparently, this is a much more severe issue with cast iron where you can see these issues even with a 12 inch skillet on a 10 inch induction hob.

With a traditional gas stove, the direct heat from the flame will still heat the skillet base well even if the flame has a somewhat smaller diameter.

Skip to 24:23 in the video.

I use cast iron on my Wolf induction cooktop. The pans are old Wagners Griswolds, & some ancient gate marked things, plus a Tramontina 12 inch enameled braiser. The Wolf induction coils appear to be 8 inch diameters. The 11 inch hob is also 8 inches of induction except when I put it on Boost mode -- then I get a 10 inch diameter. But Boost is too hot for cooking, though great for getting a big pot of water to boil.

I don't find using a 10 inch or 12 inch cast iron pan to be a problem. Yes, the outer inch or so isn't as quite as hot as the interior, but it still gets plenty hot enough to cook foods thouroughly. It's not a radical difference. If browning beef chunks, at some point I stir them to ensure uniform browning, moving "pinker" chunks to the center. Same with chicken thighs -- rearrange them when needed. They are pretty much evenly browned, but not perfectly. Would anybody refuse their meal because of that?

You can use your oven's air fryer or convection roast mode if you absolutely need perfectly uniform browning. You can deglaze that pan easily too.

I don't understand how a ring of flame wouldn't create hot spots & cool spots also. With induction there's no cooler air flowing into the air gap like with gas. With induction, the heat eventually spreads to the outer limits of the pan & heats the glass below. When all gets hot, it stays hot from inertia.

I use my 10.25" and 8" old Lodge cast iron frying pans without issue on my induction stove, and have been for almost 8 years. No problems They're not entirely flat on the bottom, but they work well and the small indented logo doesn't seem to be an issue.