why the Giuoco piano isn't played?

Because Black achieves close to an equal position

Oh, here's the Petrosian game I was referring to:

I play the Italian rather frequently and here in Wisconsin it's undergoing something of a renaissance...

I've always liked the Guitar better.

Hm, the Guitar Piano...

Honestly, I was trying really hard to reason why black played that, and in my notes noted it was weak at worst and at best a faulty defensive preparation.  As for the Bxc3 yeah, that was premature and looked like a positional mistake but didn't want to sound like I think I know better than masters, so thought there was at least enough merit behind it (though analysing from the white side wasn't my problem) to be played on Petrosian's level to justify it (somehow).  I still won't take up the four knights anytime soon, but I liked looking over that game and taking note of plans, imbalances, etc. 

The idea of giuoco piano is bringing the pawn to d4, then d3 is a bad move, especially after the knight comes into the board.

The Italian Game isn't as strong as the Ruy Lopez, but is still pretty dangerous if White knows what they are doing.

In addition to the Moller Attack lines with 3...Bc5 4.c3, there are the Giuoco Pianissimo systems with d3 and c3 (which should not be underestimated), and also my favorite, the Canal Variation with 4.d3 Nf6 5.Nc3 d6 6.Bg5. The Canal is completely equal if Black knows their stuff, but that doesn't prevent many players from getting into hot water against it. Check a good database, and you will see many examples of 2400+ players getting smoked. Black should eat White's LSB with his QN, but even then there are still some chances to play for a win...

For Giuoco middlegame ideas, I highly recommend GM Khachiyan's lectures on this site.

I think there are way too many lower-rated players who use the Sicilian. I believe everyone should answer 1.e4 with 1...e5 until they are at least 1600. The problem, in my view, is that a lot of teachers don't spend enough time on fundamental positional play and maneuvering, and they don't show their students enough classical games. 

So students get the idea that the double king pawn openings are "boring" and don't appreciate the subtle play that can arise from the Four Knights or the Hungarian Defense, for example. Lots of points to be had by outplaying such opponents!

I find the sicilian the easiest opening to beat at my level

It's easy to misplay at any level.

Has theidoogy been here since 2012?

I sometimes play Giuoco Pianissimo, But I prefer Fried Liver Attack after coming to Italian Game.

The real question is, did theidoogy believe that the world was going to end in 2012? O_o

Ok but what if 11...Na5?

Qb3 is bad here bcoz u allow black to trade your LSB against Nc6.

Qb3 must be played at move 10...

The footnotes in ECO for this system go back to 1600. It's a great system that has many interesting variations, including the Evans Gambit and the "pianissimo" (d3) lines. I daresay, it's "fun" to play.

I feel like its the opening every learns first as a kid, so they give up on it as they get older in favour of newer, more so called "exciting openings". So they never really  learn to play it well, so when they eventually develop and get better as a chess player, they regard it as boring as when they were playing it they were weaker players, so they never really had the creativity and ideas in  the first place making it boring. For example If you study on that  the game between Nakamura and the south African chess hustler , they played the Italian game I was amazed to see the level tactics involved  in the game and creativity which I never before once considered. https://www.youtube.com/watch?v=Mc7gz7Dzz0Mhttps://www.youtube.com/watch?v=Mc7gz7Dzz0M