A lot of valid points given: healthy foliage, vigorous plants, consistent bloom patterns (unless we are talking colour break, in which case you do want an inconsistent pattern but the colour break itself should show on every bloom). If the plant multiplies well and produces fans readily, bud count is less important because the clump will be a standout. Taller scapes, yes: keep the blooms up where they can be seen.
Less branching can be forgiven but buds that hang on each other and won't open is an issue. Rebloom may be great in the south, but in the north our season is too short for most rebloomers to actually rebloom. So bud count does still matter, at least in that regard: if you have a choice between a daylily with a count of 15 vs. 40-plus, it matters.
A bud count lower than 15 had better be the most spectacular pattern I have ever seen and, among newer daylilies, I have gotten to the point where I want 20 or more. (I did get a new daylily this year with a low count, the hybridizer plans to register it... and it is spectacular.) So there could be an exception to a "rule"...
Sturdy scapes is a 'must' - bloom count is irrelevant if the scape flops and the flowers are in the dirt. Fading and water-spotting is a negative, too - the bloom should look as good in late afternoon as it did at nine in the morning. Fragrance, while nice, is a bonus not a necessity. For myself, my own standard would include: would you buy this plant from another garden / nursery / hybridizer? (Would you replace it if it died...?) If I can't say 'yes' then why would anyone else want it?
