^Except most of the references to neutronium, especially its use in DS9, make no sense. Neutronium is the stuff neutron stars are (partly) made of. It's so dense that a spoonful would have the mass of a mountain. Its own gravity would pull it into a sphere, so it couldn't have the shape of the Doomsday Machine. And if you made a door out of the stuff, like the door to the Dominion stronghold in "W.hat You Leave Behind," it would instantly plummet through the planet's crust and sink to the center. That is, if such a small amount of neutronium could stably survive at all, which it couldn't, because its own internal degeneracy pressure would cause it to explode back into normal matter.
Unless you can manipulate mass and gravitation to a large degree - such as when you generate a warp field, something everyone and his idiot brother can do in star trek.
About transphasic shields - their breaking thermodynamics is minor by comparison to warp drive, cloaking, transporters, etc breaking various other physical laws.
And explaining these shields in half-fantasy physics terms (this is star trek physics) is a LOT less convoluted than explaining some of the other trek tech.
You're welcome to try to come up with a relatively more plausible explanation for various trek tech.
But, if you want to be self-consistent and you claim that transphasics must be censored out of trek due to their implausibility, you should claim a LOT of other trek tech must likewise be censored.
I don't see you advocating warp drive or transporter censorship, Christopher.