This is been keeping me up every night for the past few years:
Why can’t EdgeSrf work with a single closed curve?
Hello - that is simply not what it is designed to do - it combines the structures from opposite pairs of input curves. If you have a single closed curve, PlanarSrf or Patch are your options. Surfaces are inherently four-sided, so a pair of curves or four curves is reasonable input for an EdgeSrf, which does no trimming. Three curves also works ok in some cases, odd in others. The nice thing about EdgeSrf is that given good clean input, it makes a very simple, clean surface.
-Pascal
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You can always Divide/Split the single curve into two, three or four curves and then use EdgeSrf.
The divide part has always left me puzzled why.