@goedric It seems for most varieties that pollen is usually or always infertile. Was wondering if this is because he beards are somehow mutations of something involved in anther/pollen development.. or some other biochemical cause... or perhaps historical genetic constraints.
The genetics of infertile pollen in daylilies has not been studied, (or at least published) to the best of my knowledge. So it is not known why many diploid daylilies with petal protrusions/excrescences also are pollen sterile. Although it is possible that the petal characteristic in some breeding lines is genetically linked to pollen sterility it is not likely. It is probable that due to inbreeding, the pollen sterility that is present in 'Bee's Bettie Sue' has spread and increased in frequency within that breeding line.
In other plant species pollen sterility can be a classical Mendelian (nuclear) mutation. That is it may be inherited in some cases as a "dominant" and in other cases as a "recessive" and both parents contribute equally. However many pollen sterilities are inherited only from the pod parent and are cytoplasmic.
Michael's Sword (MS) has produced pollen fertile offspring when apparently used as the pod parent. So it is unlikely that the pollen sterility is cytoplasmic. That leaves "dominant" or "recessive" inheritance. If it is completely "dominant" then approximately one half of the F1 seedlings from a cross of MS (assuming it is heterozygous) with unrelated daylilies would be pollen sterile. If it is completely "recessive" then none of the F1 seedlings from a cross of MS with unrelated daylilies should be pollen sterile. One quarter of the F2 seedlings from those F1s would be expected to be pollen sterile.
There is one potential catch. The information available so far indicates that the petal characteristic is both variable in its expression and incompletely penetrant. That means there are daylilies that genetically have the characteristic but that may never show it. Which in turn means that there are daylilies that may be related to MS that do not show the petal characteristic but that may have the pollen sterility, possibly in a hidden state.
When characteristics are variable in their expression and incompletely penetrant it is useful to find outcrosses that increase both the expression and the percentage of offspring that show the characteristic and to minimize outcrosses to daylilies that do not increase those aspects.