As I watch flutists (don’t get me started on “flautist” please) play it seems to me that the position is rather awkward, of the left arm obviously, but also of the right.
I have wondered about this ever since a friend at Case Western told me about a physics colleague decide to reinvent the recorder based on modern acoustic theory. He did so and produced a recorder that, to my friend’s ear was indistinguishable from a flute. It was direct, of course.
I’ve wondered that too, but it seems that would help you hold on to it, since it’s not going to be as easy for it to slide out of your hands. Probably more importantly, though, is that other than being cocked way over to the side, it’s being held with the same grip as any other woodwind.
I have no idea if it shares any fingering with any of the other instruments that are held upright. If it does, that would certainly make it easier to move from one to the other.
Assuming I understand your question correctly, it’s simply because allows the embouchure hole to be along the tube. To use the same “blow across the hole” concept while allowing the instrument to nearly vertical, they’d need to have an additional bar perpendicular
The recorder does use a similar principle, but it has a different embouchure type. It’s a whistle: you blow into one hole that restricts the air and pushes it across another hole. This makes it much easier to produce a sound, but I would assume it would add a lack of control. The first hole is a fixed size, unlike the mouth.
Not necessarily, you could have a J-shaped flute where the *embouchure *is transverse but the body is vertical (possibly with a small counterweight on the opposite side of the J so the flute is nicely balanced). There are flutes for kids where the body of the flute does a sort of Ʊ next to the *embouchure *so that their tiny arms can more easily reach the keys (which are towards the end of the instrument) without reaching too far - I’d assume some length of tubing is necessary before the keys for Acoustic Physics Reasons.
It should be noted that the mouthpiece for the recorder (the structural reed) is called a fipple.
Moved from Great Debates to Cafe Society.
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I’m not trying to mock the original question, but one might as well ask why violinists don’t hold the violin vertically, like a cello or a double bass. (BTW, I’ve played the flute for over 50 years. It is not that uncomfortable or awkward to hold. I’d rather hold a flute than have a baritone sax hung from a strap around my neck or have to deal with a trombone.)
You’re just flauting tradition.
It’s not really a similar question though, because there isn’t a type of violin that’s “built sideways” compared to the usual one.
If a car analogy isn’t immediately rejected as a bad idea, I’d say you might be able to compare the transverse flute with the manual transmission, and the recorder/block flute with the automatic. Not in any mechanical sense, but because the transverse flute has more flexibility, more control for the operator, and proportionally more chances for operator error.
The article “Flute” on Wikipedia has a section called “Acoustics”, and the fairly short first paragraph may be informative enough without getting into unwanted detail. I started trying to restate it and then realized that whoever wrote it already did a much better job than I would do.
The lil’wrekker played flute and piccolo in highschool orchestra. She’s a left-y. We toyed with idea of her learning left-handed. The band director was sure she’d learn it better right-y. It worked out, she was 1st chair for 2 years.
Meh… A trombone makes a flute look like the cockpit of a 747. Sure it’s bigger, but a trombone is just a piece of pipe that can be lengthened by sliding. Very few instruments can claim to be easier to duplicate than the trombone, by buying common items at Bob’s Plumbing Supply. 
(Even professionally-made trombones have very little done to them that Bob himself wouldn’t recognize. He would see the way the slide fits together, understand perfectly, give a low whistle, and say “That’s some nice work!”)
The flute doesn’t rely much (if at all) on having a dominant hand. The confusion of being backwards to everyone else, and especially the confusion of having to translate every instruction you get, would far outweigh any advantages. I’m not even convinced that there would BE advantages. Come to think of it, I’m not even sure you could make a flute work, holding it the wrong way around. You could with a recorder, but the advantages would again be minimal to none.
Remember, the flute is played by blowing over the hole (like puffing on a jug in a jug band). Other woodwinds made sound by blowing through a hole (usually into a reed).
The sound is changed by changing the length of the column of air. If you put a bend on it, the air column would end at the bend. The keys would have minimal effect on the sound. So in order to work, the flute needs a straight column.
You could put the hole at the end of the column and hold it like clarinet. But I would suspect that it would be awkward to play like that and certain techniques would be difficult to manage.
Yeah but see, I flunked Physics 101 for a reason, mate. It’s not that I’m dumb, it’s just that I can’t get involved in these things without flinging the book 50 feet away while screaming “UGGGGH WHO CARES !?” within 20 minutes. And some people do care, and I’m grateful for their sacrifice. I’ll happily sit on the shoulders of these giants and grill s’mores on the fires burning in their synapses. In the end, I’ll just take their word for it. And, fair’s fair, should these guys ever ask about etymology minutiae or historical trivia, I’ll bore them to tears with my brand of boring knowledge.
They haven’t yet :(.
But there already are bent flutes, and they work. See Wikipedia at “Bass flute” for a picture.
The bass version of a recorder is also bent - this seems to be a thing about bass instruments, and I wouldn’t be entirely sure that what works for a bass instrument would be scalable to a soprano one.
If you accept that the angle of the flute is influenced by the needs of the embouchure, the next question that occurs is ‘why have an embouchure rather than a plain whistle end?’ I think the answer is ‘it’s more versatile’. I know you can change pitch with the same fingering on a flute by blowing differently - I don’t think you can do so in a controllable way on a recorder. You can make it ‘squeak’ if you’re a bad recorder player, but I’ve never heard a recorder player set out to play a high octave that way - the instrument is restricted to the octave it happens to be tuned for.
I note also, that all the wind instruments in a standard orchestra have some sort of complexity to how they’re blown - reeds, or trumpet mouthpieces or whatever. I think the very simplicity of the recorder gives it a reputation problem - it’s so simple even six-year-olds can play it, so most people’s experience of the instrument is the sound of a class of second graders shrieking away on crappy plastic instruments with ‘three blind mice’. To become a ‘serious’ instrument needs some complication - the evolution to transverse flute with embouchure and keys seems to be how the medieval recorder managed that.
(Not that I 'm arguing that a recorder can’t be a ‘serious’ instrument - a full set of soprano to bass recorders can produce some very nice music indeed. But not many serious musicians are really working with the instrument)
Rather, I think that the answer to “why does a flute have an embouchure” is “that’s what makes it a flute”. Instruments with other kinds of mouthpiece exist, but those other instruments are called something else, “clarinet”, or “recorder”, or “oboe” or whatever.
So we found out. It worked out ok for her.
The contrabass flute is parallel and it has a couple of bends in it.