My experience with eggs is the opposite. Eggs stick when added to a cold pan. Letting the pan get really hot first has stopped eggs sticking for me.

The quality and state of the cast iron pan makes a big difference.

If you have a good seasoning then less oil while cooking is needed. If you have a new pan with a rougher surface then using a steel spatula will smooth out the surface texture and improve performance (without making it too smooth where seasoning won't stick).

There's a lot of varying advice on cast iron, but the prevailing wisdom seems to be that if you keep using it then the pan will improve.

I actually machined, de-oiled, and polished a cast iron skillet I bought in the the supermarket. After seasoning with flax oil it was effectively non-stick. I would use a single pat of butter for 3-4 eggs. Regular use with heat control and edged steel spatula are essential to maintain seasoning. Also make sure helpful people don’t try to wash it in the dishwasher. I would just wipe it out with a paper towel and soft salt, sometimes heating it the oven with a bit of oil to restore surface smoothness. I also have a ca 1875 Swedish manufacture cast iron skillet which didn’t seem to need any machining.

Cast iron doesn’t seem to work as well on electric stoves: Temperature control is problematic. Perhaps induction heating would be more effective?

I got mine working fine on my electric after some experimenting with what heat to use.

You probably want to use a wrought iron pan for that. They can be really cheap (starting from less than 10€), are indestructible (they don’t break if you drop them) and can be much thinner than cast iron. They are better for eggs, where you want to change the temperature during frying very quickly.

Yes, a good Matfer or Solidteknics carbon steel / wrought iron / blue iron pan is fantastic for eggs, omelettes, and crepes. Matfer as a French brand even has specific crepe and omelette pans made this way.

The only downside to a Matfer, or any other carbon steel pan, is that you need to be prepared to season it yourself. They do not come pre-seasoned like most cast iron pans and it is a good bit of work. Having said that, I absolutely love the one I have and plan on buying at least one more in the future.

Any reasonably well cured cast iron barely needs any oil