IMO, magnetic pan sides make little if any practical difference one way or the other to having hot pan sides.

Consider how rapidly that induction fields diminish above the cooking surface.

Put a kitchen towel under the pan. The pan will usually heat with one thickness of towel between it and the burner surface. Fold the kitchen towel over (two thicknesses) and the pan won't register. The field does not reach very high up the sides of a pan. At least, it does not do so with my pans on my induction cooktop.

You can find a further discussion of the absence of side heating from induction with pressure cookers in this explanation by Laura Pazzaglia's of the mechanics of using pressure cookers on induction versus gas and radiant electric burners.

I'm not entirely sure what you meant in your last question where you asked about "entirely magnetic" pans. Did you mean to ask about pans with magentic metal in their sides (which is to say, disk-base versus clad pans) or were you asking about pans made entirely of magnetic metal (such as carbon steel, cast iron, enameled cast iron and/or cheap thin enameled steel like Graniteware?)

If you meant to ask the latter question -- say, whether you might want to
go entirely with LeCruset enameled cast iron or Matfer or DeBuyer
carbon steel pans --- I'm sure you can get a ton of responses on that
point.

In the meantime, let me offer this about heating sides of pans on induction. My cookware includes some cast iron pans, some All-Clad (fully clad), some Sitram (disk base with rather thin magnetic sides), and a non-stick set of Circulon Premier Pro (sold relatively inexpensively by Costco, having anodized aluminum bodies with an magnetic slug in the base). What I have found is that the sides of pans in the sets with the highly conductive aluminum up the sides (All Clad and Circulon) heat up a lot more quickly that those with only magnetic metal sides (the cast iron, the PCs, and the Sitram). Here's an example of a test I ran for myself a while ago. Put an inch of water in the cast iron pans or the disk based Stiram. Brought the water to a boil on induction. Used a Thermapen to measure heat levels. When the bases of the cast iron and Sitram pans were 200° F, the side were considerably cooler, around 130° right above the boiling water and less than that the further up the sides that I measured.

This was not a precision test, of course, but you get the idea that heat on the sides does not spread rapidly through induction heating of the bases.

Thanks for the link - it's interesting; it makes me realize I might need to learn to cook a little differently.

In the last question I asked, I was actually wondering about the difference between disk-based pans and all-clad pans, but I was trying not to use the term "all-clad" because I don't mean the brand, just the concept. You're right, of course, that a cast iron Dutch oven is also entirely magnetic, but I wasn't thinking of my cast iron skillet or casseroles. Should I be looking for all-clad pots, or does that concept not differ much with respect to cooking than the disk-based pots?

Just call them "clad" pans and everybody will know what you are talking about.

For a lucid and straightforward discussion of clad versus disk-bottom pans, I recommend that you check out Franz's blog on that subject on his CenturyLife.org site.

another great link......that's just what I was looking for, thanks.