Pollinating and tagging is enough work to do, even in my small garden, without collecting all of the pollen on all of the daylilies first.
I might collect pollen prior to making crosses
sometimes for a special daylily (usually a new plant or a seedling), but that is because I am going to save the pollen in gel capsules in the fridge.
Most mornings, it is a race to get the pollen anyway before the honeybees and carpenter bees get it all. Frequently they beat me to the blooms, or else are trying to get to the anthers and pollen on a bloom while I am trying to pollinate it!
I don't doubt that sometimes, when I am forced to use their "leavings" for pollen for making my crosses, that there might be some "foreign" pollen mixed in there.
Oh well... it keeps the seedling patch interesting...