True. All 16 gauge 870s have been made on the same frame as the 12 since 1950. Early 20s were too, but in the 60s or 70s the LW frame was introduced.
You may possibly change over a 16 gauge 870 to 20, but you'd need an old style barrel, bolt, mag tube and shell catchers.Maybe other parts also, I'm no smith.
Not a practical swap when the world is flooded with old WMs, many in 20 gauge and good shape for a pittance.
Enjoy your 16, and deal with the ammo issues.....