Currently? It provides no benefit and depending on receiver might even be negative, but if an AM receiver was designed to demodulate the sidebands independently and average their output might indeed gain slightly better noise rejection than using just one sideband. That is the idea being suggested by the person talking about a stacked image analogy.
The first step to improving AM (while making the receiver more complex) was removing the carrier wave, which is responsible for most of the transmitted energy (Double-sideband reduced carrier modulation, or DSB-SC). Then, to improve efficiency further without increasing receiver complexity too much, the second sideband is removed (Single-sideband suppressed carrier, SSB-SC - commonly just SSB).
The only benefit of traditional AM is transmitter and receiver simplicity. If you start increasing the complexity, there is no longer any point to using it.
self-nit: I wrote Double-sideband reduced carrier modulation, which is DSB-RC and only reduces the carrier. Double-sideband suppressed carrier modulation is what DSB-RC stands for, which removes the carrier.
The first step to improving AM (while making the receiver more complex) was removing the carrier wave, which is responsible for most of the transmitted energy (Double-sideband reduced carrier modulation, or DSB-SC). Then, to improve efficiency further without increasing receiver complexity too much, the second sideband is removed (Single-sideband suppressed carrier, SSB-SC - commonly just SSB).
The only benefit of traditional AM is transmitter and receiver simplicity. If you start increasing the complexity, there is no longer any point to using it.