No, there is no flaw in this, and moreover there is nothing new in this. This is how it has always been, it is not something invented recently.
In the Solar System, there are 3 Mercury-sized satellites and other 3 Moon-sized satellites, besides the Moon. If they had not been in their orbits as satellites, they might have very well been planets. Therefore the old definition of "planet" also depended on the orbit of the body, not only on the size and shape of the body.
Most of those satellites are bigger than Pluto. Triton, the biggest satellite of Neptune, had been in the distant past another planet with an orbit close to Pluto, but it was captured by Neptune and it has become a satellite. Otherwise it would have remained a "dwarf planet", orbiting close to Pluto. So Triton was demoted from "planet" to "satellite", by Nature, not by a human organization.
The current definition of "planets" and "dwarf planets" is fine.
If anything, there are too few planet classes, not too many. A more useful classification is into big planets, medium planets and small or dwarf planets, where the Solar system has 4 big planets, 4 medium planets, and a lot of small planets.
The big planets, i.e. which are big enough to retain the volatile chemical elements, like hydrogen and noble gases, not only the refractory elements, have a very different chemical composition from the medium planets, and this difference will also exist in any other stellar system that has condensed from gases like those at the origin of the Solar System, with more oxygen than carbon (there exists the possibility of stellar systems with a different chemical composition than the Solar System, formed by condensing from gas mixtures with more carbon than oxygen).