I'd honestly say it's a bit of hokum. "Prime scale" is not a standard theoretical term (to my knowledge), and the various associations of "prime" in theory don't really accord with anything this author is talking about.
But the real problem comes in the claim quoted in the question:
Remarkably enough, out of all possible scales there are only five
prime scales, in which every single note is a member of at least one
major or minor triad and which contain no chromatic semitones. All of
these scales contain seven notes. [Bolding in original.]
This is the significant claim of the page, but it's false. One could choose just about any six-note or five-note subset of many diatonic collections and achieve a scale that satisfies the conditions of the author. The "no chromatic semitone" restriction effectively rules out scales with more than seven notes.
And that's an arbitrary restriction too: why is it "superfluous" to be able to build both a major and minor tonic triad on the same note of the scale, but only if that note is the root? It's certainly allowed (by the author) to have notes in the scale that could function in two or three different triads, so why does it matter so much that you can't do that in a case where the triads have the same root? If the author is indeed interested in "harmonic resources," why are some added triadic possibilities good, but others are "superfluous"?
So, having jettisoned scales with 8+ notes with an arbitrary constraint that isn't given adequate justification, the author then proceeds to ignore 6-note, 5-note, and fewer scales that satisfy his constraints, without explanation. Why?
I'll grant that most of those scales with fewer notes don't satisfy his criterion of being a "proper mode" (a rather complicated constraint), but neither does the "double harmonic" scale he discusses and admits is not "proper." And it's even possible to find "proper" scales with fewer notes, for example the diatonic collection minus the leading tone, e.g., C-D-E-F-G-A. That satisfies all his constraints, including being "proper" (in his terminology).
And it's not even that he's tacitly excluding scales with fewer than seven notes: he explicitly earlier makes reference to the pentatonic scale as having importance. So, it's simply not true that "out of all possible scales," there are only five that satisfy his conditions.
(And honestly, I can't be bothered to check if his claims are true even for heptatonic scales. It seems reasonable that the five he quotes make sense, but I'm not convinced they are the only ones without checking. Part of it may be in the sleight of hand from where he goes from the "no two chords with same root" criterion to the "no chromatic semitones" criterion, which I'm not sure are exactly the same thing, even though he claims they are. Actually, I lie. I just tried to make a scale, and C-C#-D-Eb-F#-Ab-A is a seven-note scale that satisfies his "prime" conditions in that no notes are "superfluous" and no note can serve as the root of both a major and minor triad, but nevertheless has chromatic semitones. There are likely others. The more one digs, the worse this whole business gets.)
When the big bolded claim turns out to not only have arbitrary constraints to get there but is also literally false, it's probably time to find a better theory source. I mean, you can create whatever constraints you want to for preferring certain scales, however arbitrary. But we should at least demand self-consistency in a theoretical system.
Lastly, as to the final part of the question and what "scales to create modes from": that's up to you to figure out what you want in a scale. If you like the author's constraints and what scales the theory puts out, why not use those scales? There are no abstract "rules" for how to create scales or modes, other than your own compositional priorities.
