the "classicly" defined issue with a cloudy broth is a too vigorous boiling/simmering/cooking. supposedly this results in a lot of very fine particles / protein compounds exiting "the bones/etc" and floating around in the water/liquid.
frankly I don't know how accurate that is to the nth detail, but in my experience the theory holds up. I would further add, making 15 quarts of "broth" in a 20 qt stock pot works way far more better than trying to make a quart of broth in a sauce pan. I'm thinking it's easier to control the degree of "simmer" in a larger pot....
now, "particles in water" fall into various categories. sand will fall to the bottom. organic matter will "sorta' float around" and then there's the "colloidal" suspension - particles so fine they remain "suspended" and will not "fall out / precipitate" - fat(s) is a different matter - absence emulsifiers, they will float to the top where they can be skimmed off or chilled to solidified and removed by chunks.
Chicken carcasses are really good at producing colloidal suspensions in my house.
then, there's the "clarify" thing - clarify a broth for a consume,,, for example. which is all fine and good and likely a "required" thing in high end French soups, but actually in my feeble home kitchen, I make broths for use later in gravies / etc - roux + home made broth = really good stuff on the table.
there's a "raft" (oops, bad pun) of methods for clarifying broth. so far as I've learned, the eggs shells really only bring the residual egg white to the party. three day old dried out egg shells,,,, might not work so well - not tried that. the egg white proteins form a soft "foam" that easily traps the fine particles. as will a super fine strainer, or a coffee filter,,,, however in my limited experience, the eggs white raft is superior to any "filter technique"
done the coffee filter thing, not equal to clarifying with egg whites....