If Hornet Queen is a color pie break, why is it reprinted so often in commander pre-constructed decks?

Because it’s popular and it’s not introducing it to a format that doesn’t yet have it.

Is Hornet Queen only a break because it makes a bunch of small flier tokens? Green seems to be allowed to get flying on high MV rare creatures, like on the occasional green dragon.

Hornet Queen’s issue is that it’s too efficient in both creating fliers and in shutting down the opponent’s fliers with your own fliers.

Can tokens have abilities that are out-of-pie for the token's color if the token itself is generated by a card of a color that could have the ability? For example, if Hornet Queen were a black card, could the tokens it generated still be mono-green?

Cards can generate tokens of other colors, but that token must mechanically be something the original color can produce.

In order to keep its exact text, what color(s) should Hornet Queen be?

Black could do the exact text except the tokens would be black.

Would Hornet Queen but mono-Black be following the color pie?

Yep.

Do you think it’s possible and worthwhile to, **without** bending or breaking the pie like Planar Chaos, have a “colorshifted” theme in a set? I’m picturing things like the GDS3 “Serra Angel” in BG, a monoblack Hornet Queen, or monocolored versions of some of the appropriate-but-unique hybrid cards.

It is possible.

If you remade Hornet Queen with the exact same cmc and abilities, what colours would it be?

Either monoblack or black/green, most likely.

I don't consider it so wrong when a green creature flies. Flying is something so common that it's just everywhere. I think that flying is something that is chosen for flavor reason, because that character flies. The only things that don't fit to green are effect that grant flying or care about flying (except for flying hate), or also things that create too many fliers (such as Hornet Queen). Or am I wrong?

Green is supposed to be actively bad at flying and have very few fliers. It is first in reach and flying creature kill to have an answer to fliers.

I know green isn't usually supposed to get flying except the rare case of mono green dragons and insects, but can i request more insect tribal that includes flying? Hornet Queen and Hornet Nest are two of my favorite mono green cards despite being so close to being green breaks, only avoiding it via the loophole of insects being green.

I consider those cards breaks, especially Hornet Queen.

I just saw Ram Through, and it feels about as green as Hornet Queen. I know you guys have been experimenting with giving green still more of the color pie, and I'm humbly asking you to please, please rein it back in.

“Bite” (one-sided fight) isn’t just allowable in green, it’s primary and has been for a while. Adding “trample” to it (a primary green ability nonetheless) shouldn’t make the spell feel out of pie for green.