Weighing in here.
Both egg shells and oyster shell contain calcium in the form of calcium carbonate. Calcium carbonate is almost useless to us Human types, but its the preferred form of calcium for poultry here in the US (diCalcium Phosphate and Calcium DiPhosphate are arguably better, but are used less - expense, mostly. You say their use more around the Mediterranean basin). Of the two, because it is so much thinner and more brittle, egg shells dissolve faster in a chicken's digestion, providing a somewhat faster but shorter, calcium boost.
Calcium Citrate (the form of calcium we humans can readily absorb) breaks down much faster than calcium carbonate, and is the form recommended when you have a bird suffering some malady (like egg-binding) potentially improved by a swift kick in the calcium - but due to its rapid absorption, its not good for long term maintenance/routine shell production support.
It is well established, via study and experience, that given the choice, most chickens are rather good at self-regulating their calcium intake.
Therefore, many of us here on BYC with mixed flocks of differing age, gender, and frequency of lay (or status of molt) offer an "All Flock"-type feed with free choice oyster shell on the side. Yes, "oyster shell, oyster shell, oyster shell".
Can you offer egg shells instead??? Of course you can. Its the same calcium. SO, why don't we with the "EDUCATOR" badge next to our names do that? Because no system is 100% efficient. A bird "deposits" less calcium in its egg shells than it needs for maintaining its body and producing future egg shells. Calcium is important for a bunch of other functions. The roughly 1-1.5% calcium they get in an "All Flock"-type formulation should be adequate for maintaining body condition and routine metabolic activities, nothing more. So feeding eggshells back to the flock,
ON ITS OWN, isn't enough calcium long term. That's why we don't recommend it as part of the routine "
how to feed" advice for new owners.
Can you buy eggs and feed your birds the shells? Of course you can - but a small bag of oyster shell can be had for the price of 2 dozen eggs, and is slower dissolving (so better for overnight egg production). Is there any reason not to feed egg shells back to your flock when you are offering free choice oyster shell? Not really, there is a tiny possibility it can be a disease vector, but plenty of us do. For instance, i routinely throw egg shells back to my birds, I keep free choice oyster shell in dishes for my birds, and I made this lengthy post while I should have been eating lunch.
I then watch to see which birds run for them. (Usually, its my pekin ducks). If all the birds are ignoring the egg shells** [as often happens] but one bird, that's a bird I will pay special attention too check for illness/injuries that could result in enhanced calcium needs. and if it is otherwise healthy, expect for an abnormal calcium need day after day, month after month? That's not a bird I'll want to keep as a breeder.
**be aware if you throw raw egg shells, your birds may be gobbling them up not for the calcium, but rather for the protein in any albumin still clinging to the egg. Also, no need to crush egg shells. Bake them only if you are concerned for disease or odor. Risks of both are very, very, low.
Hope that helps answer some of your Qs,
@Clukcluks