I saw an interesting assertion recently, that resonant antennas are more efficient because they provide a better impedance match to free space at the resonant frequency. I believe that to be untrue, and that resonant antennas are just easier to match to the output impedance of a transmitter, which is almost always non-reactive. The consensus opinion of this group, as expressed by the votes on answers to two related questions, is clearly that generally resonant antennas are not more efficient.
What do I mean by "efficient", you ask? I suppose I mean efficient in terms of receiving or transmitting power. I'm talking about just the antenna, and not about any matching network or feed line that might be required to connect a real antenna to a radio.
But maybe I'm wrong, or maybe I'm oversimplifying. (There is a lot more that I don't know than I do know, and oversimplifying is how we humans make sense of the universe.) I investigated the Friis Transmission Formula, which I learned about thanks to this site, but it's no help. It introduces the idea that an antenna has an "effective aperture", which is unrelated to its physical size, but the effective aperture is a theoretical construct that is just a stand-in for the gain of the antenna. The formula isn't helpful here because the equation says nothing about gain, which is what this question is about.
So what about the assertion that the impedance of free space has something to do with the gain of an antenna? "Free space", i.e. vacuum, has an impedance, about 377 Ω, that relates the strength of the electric-field component to the strength of the magnetic-field component of an electromagnetic wave passing through the vacuum. When the electromagnetic wave encounters a conductive object then voltages and currents are induced in the object, which is how radio waves are received. I doubt that how close the impedance of the object is to (377 + 0j) Ω has anything to do with the efficiency of the reception, but I don't have enough Calculus or Physics to pick apart and understand everything about Maxwell's equations, so again I could be wrong.
So, is a resonant antenna inherently more efficient because it couples to free space more efficiently?