I am a big fan of enameled cast iron, and have not had issues cooking fish or eggs in mine. If something sticks, you can add a little fat or liquid (broth, beer, pickle juice, ad infinitum) to help loosen the stubborn item, it doesn’t take a whole lot. I like using a sizeable spatula with a pat of butter atop it and gently work the spatula under whatever is stuck as the butter melts under the food itself.
Things stick in your pan because there’s not enough fat to keep it moist. You’re essentially frying things when you use a pan, so having enough oil is essential to prevent burnt sticking food. With enough fat in the pan, you should be able to glide a fried egg around the pan with ease.
Enamel cast iron pans are excellent for deglazing as well, which’ll make cleaning them even more simple and the byproduct makes for a delicious sauce that’ll punch your meal quality up tenfold. Honestly you should deglaze everytime you cook,
Enamel stains as you use it but it’s pretty easy to clean with Barkeeper’s Friend (either the powder or gel work, though the powder will last you an eternity longer than the gel). Outside that, the exact cleaning method you stated works.