Your observation is correct, but the reason for this transition is fairly prosaic. Coupes represent a type of drinkware that has been in use in one form or another since the 1630s. Also, most pre-20th-century sparkling wines were generally sweeter and less carbonated than what gets sold as "champagne" these days. Based on a casual survey of artwork and advertising, sometime in the late 19th century or early 20th century,we see a shift towards the narrow tulip-shaped kinds of wine glasses that are popular today. The current association of champagne specifically with narrow, flute-shaped glasses and also with celebratory occasions, seems to have become popular sometime in the 1930s.

I suspect, but cannot prove, that the decline in popularity of the coupe is partially linked to the shift in popular types of champagne towards being dryer (less sweet) and more highly carbonated than had previously been the case. A taller, narrower glass would help the beverage remain carbonated after being poured.

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