Why they last the way they do
Because the head is made of many separate flowers, it does not fail all at once. The outer florets go over while the center is still opening, which is why a spent daisy looks ragged rather than collapsed, and why picking the tired outer petals off a chrysanthemum genuinely buys it another day or two of looking respectable.
It also means the head keeps working after cutting, and working costs water. This family drinks harder than almost anything else in the cooler. Sunflowers are the extreme case and can empty a vase in a day, but gerberas, dahlias and zinnias are all thirsty. Underfilled water is the single most common reason a florist thinks they got a bad box.
The stems are the other half of the story. Many are hollow, soft or hairy, and all three foul water quickly. Dahlias and zinnias turn a vase cloudy faster than any rose. Strip everything below the waterline, change the water rather than topping it up, and the difference is measured in days rather than hours.