It should include pop-ups though if you want the data the OP is looking for.
Fly ball pitchers are also pop-up pitchers. More balls in the air = more chances for them to not leave the infield. That said, the difference in the amount of these "automatic outs" (if only) is probably so small that it's not more meaningful than, say, strike out rate.
Being a fly ball pitcher is not really a red flag in the sense that ground ball pitcher = good and fly ball pitcher = bad. I think the assumption you're making is that every fly ball is hit hard. They're not. You want pitchers who don't give up hard contact.
Yup.
Our P1 gives up mostly fly balls. Our P3 gives up mostly ground balls.
But our P1 has a better ERA, WHIP, BAA, Ks, etc. etc. She also pitches the harder games.
The stats might be interesting, but the better pitcher is the better pitcher. And that's determined without the GO/AO ratio.