It's actually a pretty old way for Black to meet the Ruy Lopez. I'd say it's not very popular because it makes it hard for Black to develop his dark-squared Bishop and constricts the position. It is playable, though.
why no cozio
In principle i like it, and it's for certain something you could play without many fears. However i think the consensus is that with precise play W has a persistent edge (if i remember correctly the most precise move is 4.c3), and more in general B sometimes has to play very immaginatively to hold the balance. It's not such an easy defence to play.
Correction: 4.Nc3 is supposed to be the critical move.
-4...g6 5.d4 exd4 6.Nd5! supposedly starts a very strong attack.B has to find the one and only precise path wich leads to a slightly worse position in a sea of forced losses. Not unplayable but not pleasant either.
-4...Ng6 has been played quite a lot by a played named Arkhipov, but 5.h4(!) is considered very dangerous. Maybe you can look at his games.
I don't think the cozio is such an easy and theory free defense to adopt, but several GM have tryed it in the past and there is still room fore improvements i guess.
If you need help, please contact our Help and Support team.
why is the cozio never seen? at most levels its impossible (with correct play as black) for white to get anything more than a small edge. i like
it because its rich and new