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My leap into this discussion is between a guess and an opinion, but the subject is interesting.
I just looked up the 6V6, since it was mentioned, in the RCA Receiving Tube Manual, and its plate runs between 50k-ohms and 80k-ohms, which is way higher than the 3k-ohm antenna impedance mentioned by Radio8z.
When power is being transferred in a circuit, whether its a transmitter/antenna or an amplifier/loudspeaker, the most efficient transfer requires a true impedance match.
Based on my reasoning, a tube circuit would not have any advantage over solid-state, but the matching between plate and antenna would be a different batch of parts.
Tubes really get fun when you can crank up the plate voltage and get orange and blue glows from the plate.