Red wine glasses in particular are shaped to be filled to the widest point, allowing the greatest surface area in contact with the air and a narrow opening to stop the scent of the wine escaping.
Red wine can also have a sediment at the bottom of it, particularly if you take your time with a glass. Having to tip your head back to empty the glass, as you describe would mean you would get a mouthful of that, and it isn’t pleasant. The design encourages you to leave a small amount of wine at the bottom of the glass to spare you the taste and inevitable black globs in your teeth (and probably at certain times would have way of judging someone’s etiquette and breeding. Refined palates would be educated to know you don’t drain your glass, etc).
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