You forgot the "L" part of the LC filter. A shunt capacitor by itself does reduce harmonics, but adding series inductance makes it far more effective. And then there are tuned LC filters that specifically block or shunt a harmonic.
LC filters don't make sense at low power levels, but do make sense at high power levels. They are sometimes used in commercial and industrial settings. Presumably, they could be used for residential if there was a real need.
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To my surprise, shortly after Naomi Wu gave me a bit of fame for making good use of solar power, Allie Moore got really jealous of her...
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