The Copernican model was heliocentric, surely? It placed the sun motionless at the centre of the universe. That makes the sun anything but a normal star.
The copernican principle is separate from the model. Basically it says that our position in the universe is random - we don't exist at the center of the universe.
"Hermann Bondi named the principle after Copernicus in the mid-20th century, although the principle itself dates back to the 16th-17th century paradigm shift away from the Ptolemaic system, which placed Earth at the center of the universe. Copernicus proposed that the motion of the planets could be explained by reference to an assumption that the Sun is centrally located and stationary in contrast to the geocentrism. "
"Hermann Bondi named the principle after Copernicus in the mid-20th century, although the principle itself dates back to the 16th-17th century paradigm shift away from the Ptolemaic system, which placed Earth at the center of the universe... Copernicus himself was mainly motivated by technical dissatisfaction with the earlier system and not by support for any mediocrity principle."
Copernicus' solar-system model is entirely separable from any assumptions about star size distribution, and the latter was apparently not a concern of his (nor do I recall seeing anything to the contrary elsewhere.)
On account of this separability, the mediocrity principle cannot be used to eliminate heliocentric models of the solar system from consideration, at least unless there's good evidence for it.
Nevertheless, the presumed huge size of the stars was seen as more or less of a problem (depending on which way one leaned on the heliocentricity issue), but it turned out that the apparent size of the stars was merely an artifact created by diffraction (the Airy disk) [1], making it possible to hold both that the sun is well within the range of stellar sizes and that other stars are far enough away that their parallax is difficult to observe.
That sort of makes sense but the comment I replied to was still mistaken in linking the 20th century "Copernican principle" to debates in the time of Galileo.
IMO calling something so greatly at odds with Copernicus's model the "Copernican principle" is misleading (if not outright nonsensical) and explains why the commentor I corrected confused the two. What a good idea to name something completely at odds with Copernicus's view of the universe after him.
Its like "Gell-Mann amnesia" but without the humour or self awareness.
