As tattrat said: it has to do with emulsion.
If you clarify the butter you basically remove impurities (remains of whey, water,...) and you keep the pure oil from the butter. Then the eggs in your sauce can do the rest.
It's the same as butter with eggyolks is tasty, but would never yield you a mayonnaise
Tonight let us eat, drink and be merry for tomorrow we die.
Another vote for not bothering with clarified butter for Hollandaise - or any other emulsified sauce for that matter. I've been making them for 30+ years with regular butter & they've always turned out just fine.