That's just saying the same thing twice. Reskinning has clear merit because I do it all the time to create my concept of a character from existing classes. Not just D&D.
It can be fantastic, though the availability has varied in D&D over the editions. In 2e, for instance, if you wanted to re-skin the cosmetic look of your fireball, you actually cast a 2nd level spell, called Sense Shifting, that'd do it. (I'm pretty sure I'm remembering that right - one of my players
loved it.)
In 3e - AFAIK, for the first time - you, as the player, explicitly had the option to re-skin your character's personal appearance and his gear. Thus, bastard sword & glaive could equal katana and naginata. That never caused
any controversy, at all.
But, it was late 3.5 and some fiddly feat called Spell Thematics before you could much mess with how your spell effects looked.
4e expanded on that, letting you re-skin prettymuch anything/everything about your character,
short of changing keywords. So, even then, you couldn't re-skin your Sorcerer as a Psion.
AFAIK, 5e is less permissive than that with re-skinning, from the player side. The DM, of course, has carte blanche - he can not just re-skin, but re-muscle, bone, and vital organ whatever he wants.
"Anything can be reskinned" is actually the bad argument because it acknowledges the lack of need for the psionic classes. Demonstrating that point with other classes doesn't disprove that it also applies to psionic classes; it reinforces it.
The point is that "you can already (sorta) do it by re-skinning (if you squint real hard)" is not a valid bar for psionics to clear for inclusion. Because if it were a valid bar, it'd've blocked most of the PH classes. You'd prettymuch have had a loosely-defined Fighter and Magic-User.
Re-skinning as an excuse to exclude a concept with a history that encompasses virtually the entire history of D&D is also just really, really weak. And, is moreso in context when you consider the conceit that 5e classes are designed
concept-first.
Re-skinning is
mechanics-first/concept-last design.
And yet they do it. That demonstration of manifesting power is common in the tropes. Glowing eyes and pointing gestures and more. Bleeding noses if you prefer. It's also D&D.
Well, it's not D&D, per se. D&D VSM is still fairly well defined. V are audible, strange-language, incantations; S are visible, conspicuous gestures; materials range from the cheap/mundane/inconspicuous to the expensive and/or eye-catching. And they're hard /requirements/.
Typical uses of psionics encompass such things as 'looks of intense concentration,' sweeping gestures, and secondary manifestations (lights flickering, wind, objects levitating). But, I can't think of an example of "I can't use my psychic powers with my hands tied," the closest thing I can come up with for a verbal requirement is in giving commands to a dominated target, bordering on hypnosis, really. They're more like accompaniments than requirements.
That argument that there wasn't such a tell or display of power didn't exist in 3e or 4e. There were descriptions on demonstrating that manifestation.
3e made it very clear that psionic powers had manifestations, so they were obvious. I don't recall if it had requirements. In 4e, players described powers as they liked, but it was always obvious you were using a power - 4e just played very 'above board' that way, regardless.
Psionics is Different was an optional rule.
And 5e, the Big Tent, DM Empowerment, edition, is big on optional rules.