What material is best for cast iron handle covers

I also have a glass-top stove at home. So far, I really like it: the heat is very even and there is good heat transfer, provided the pan makes good contact with the surface (one skillet I have has a bit of a lip, which makes it heat more slowly).

I've slapped skillets and pots full of water around on mine, and have yet to break it. I'm probably more careful than I would be on a metal range, but it seems sturdy.

But to your points:

1) There is no way cast iron could melt the glass. Iron melts lower than does glass (1200*C vs. 1500*C), so before you manage to melt your stove, your pan will be a puddle. It may, however, be possible to deform the stove top if you let an empty pan heat for some time. I don't see why this would be more of an issue with cast iron than with any other piece of cookware.

2) A heat defuser will work fine. Don't get the kind that is designed for use with gas, but anything else should work fine.

3) The burners on my stove are smaller than my skillet, so I find I need to move the skillet around to heat the edges. Also, flat-bottomed pans and pots seem to be much more effective on the flat glass top, as conduction seems more effective than radiation here. I polish the bottoms of my pots to get better heat transfer, although this is just me being anal.

Also: cast iron can't scratch glass. Glass is much harder than iron (see this wikipedia article), glass having a 6-7 on the Mohs scale, iron having a 4.

What is the advantage of a steel skillet over a cast iron one? I currently use cast iron for most everything and am curious what I might be missing.

Pan sauces made with wine, vinegar, or any other acid are better in stainless steel. If you put any acid in cast-iron, you are harming your seasoning, and leeching iron into your food. This will affect the taste of your sauces, I find pan sauces taste metallic when made in cast iron.

Stainless steel also heats up and cools down much faster than cast-iron. This is great when you need quick heat, or fine control of your heat. You can also plunge a piping hot stainless pan into an ice-bath without cracking it in half.

If there's an advantage to getting a steel skillet as well, what would be recommended?

Go with a a bonded stainless-steel pan with an aluminum core. The most well known manufacturer is All-Clad. The stainless steel exterior is great due to it's non reactivity, you can literally put anything in it. The aluminum core distributes the heat much more quickly and evenly, minimizing hot-spots.

Is a steel skillet good for cooking omelettes?

Not in my opinion. I go with a non-stick pan every time.

I have to recommend sticking with a nonstick pan for eggs. There's simply nothing better, although well seasoned cast iron comes awful close. If you're spending more than $20 for a nonstick egg pan, you're doing it wrong. You don't need Calphalon, or any other big name for a good nonstick pan. Go to a restaurant supply store if you can and buy a cheap one there. With care it should last you 2-5 years depending on use. I found my current one at a Bed Bath & Beyond.