For the longest time after I started growing daylilies, it never occurred to me to check the parents of any of the plants I had. Heck, I was just thrilled to be able to ID the plant. If I already have a named daylily that performs well, not knowing the parents does not bother me in the least. If I have a seedling that I do not know the parents of (I have lots of them due to critters digging up plants and tags) it annoys me to no end. I almost feel the seedling is not worth fooling with if I don't know the parents.
Now if I am ordering a new plant, I much prefer to know both parents, and it will sometimes make or break the order. But some plants are so coveted for their particular traits, I would not let not knowing the parentage interfere with the order.