Polymerous said:
As for leaving the scapes on, in hope of sideways branches with buds growing out from the lower bracts.... Wow, that's another thing that I had never heard of. Sometimes the deer will leave a tiny bud or two left on a scape, so I leave the scape on the plant to grow the bud(s) (every bloom is precious!), but I have never observed anything coming out of the lower bracts. 
Maybe this is climate specific, or needs some particular cultural practice to encourage?
It may be cultivar specific, or related to timing. Perhaps it depends if the remaining bract would have produced a side-branch in any case. I haven't looked into it that thoroughly but will observe more carefully this year, although for the most part the deer eat down below the lowest bract anyway in which case there's no hope for that scape. I use a deer repellent so don't usually lose many daylily buds.
I looked at some unchewed scapes yesterday and noticed that some had the beginnings of a budded branch emerging from a lower bract axil. On another one (a close to species type) that had been chewed, all buds gone but with branches and bracts remaining, the scape is dying back so that one isn't going to do it. I have seen it happen though, and it looks pretty weird with the flowers all on a single sideways branch and nowhere else but they're flowers I wouldn't have got if I'd cut off the scape
.
I think the bottom line is that if the scape isn't eaten down past the first bract then you've nothing to lose by leaving it for a while to see if it will branch.
