Banana peels should be completely (done) composted before use in soil. Egg shells don't need to be and do not take a very long time to become available. A little is available at a time making them a preferred source of calcium. The last thing you want is an overdose of calcium all at once or to have to keep watering your plants with this and that trying to guess or measure nute levels unless you're doing hydro of course.
Brown material on the other hand, can be put in the soil without composting first. Coffee grounds, peat moss, etc. but can acidify the soil. If you have egg shells in the soil they will break down faster due to it and can help to keep pH in check.
However the wild card is your water supply. Rain tends to be slightly acidic but municipal tap water tends to be slightly alkaline. If you don't have much raw brown material in your soil and always use tap water then your egg shells are going to take a lot longer to break down, but then all mineral availability will be lower in that case too, and yet some people have hard tapwater with minerals in it including calcium so consider your own specific situation as to what your soil needs.
Personally, I reuse the same soil in pots every year but amend it with compost, raw materials like peat moss and coffee grounds, and a ratio of about 1 ground up egg shell per gallon of soil but I don't try to powder the egg shells, just get them to about 2mm diameter.