I'm familiar with impedance matching and the resulting efficiency. But still - If free space is 376 Ohm then why not match it to this impedance?

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Good point. I believe that 50 ohms was selected because it was efficient and practical to build 50 ohm coax.

Antennas are actually designed to be matched to free space intrinsic impedance of 377 ohm. They are basically working as a matching network that converts that 377 ohm down to 50 ohm. Good question!