Oh, this is my favourite area of study, thank you for bringing it up, and it's a shame I'm currently ill so this may be rather feverish and rambling but I will try to corral it.
Space-saving makes k = p
I agree that space - or lack thereof - may trigger a certain gallows. Quite a few people have proposed this before: I think Philip Neal pointed out that the ornate gallows tend to have more space above them, and someone else whose name I don't recall said it in an old thread of this forum.
I don't think it's ever been quantified, but a visual look at various paragraphs in the Stars folios seems to show that the ornate (p/f) or unusual k gallows are often absent when the bottom row of the preceding paragraph is vertically close and suddenly burst into bloom when it is finished and there is suddenly a nice amount of vertical space to play around in. The Voynich being the Voynich, there are of course counterexamples where there is plenty of space yet a plain k/t is used.
I wouldn't go so far as to say there is no cryptological element here. The biggest problem when suggesting p = k (or p = t, etc) is that the following glyphs do not match up. Scribe 1 in Herbal A tends to work best with a k = p mapping, because its k and its p tend to occur in the same clusters: more Gallows-ch, Gallows-sh, Gallows-o and less Gallows-a and Gallows-e. But the problem for the other scribes is that - as Rene mentions - k and t absolutely love to be followed by an e. And yet p is remarkable for virtually never being followed by an e. The few /pe/ instances may well be transcription errors for /pch/.
p = ke
--> So the obvious solution is to rework and posit ke = p for these scribes. I pick k because it tends to be suspiciously missing from the top row of lines just as p suspiciously appears, but there could be links between all the gallows.
p = ke/te has likely been thought of by a lot of people stretching back decades. Nick Pelling as far as I know was the first to posit it in writing on his blog. I was briefly super partial to it around a similar time and tried to see if the hook or flourish of some /p/ that Jorge mentioned could hide a missing /e/.
p = ke appears very pretty and convenient: it explains why we don't see /pe/ despite the multitude of /ke/, and it's easy to find valid words by exchanging /p/ with /ke/. e.g. qopol can become qokeol.
But the ridigity of Voynichese makes it sometimes deceptively easy to mix and match certain glyphs...and sometimes not. The problem is that /p/ absolutely loves /ch/. It likes /o/ as well. But it really loves /pch/ clusters. And you don't see that many /kech/ and /tech/ clusters in Voynichese. Nowhere near enough to make a mapping of k = pe or t = pe easy.
There may well be a solution to this if we then try to mutate /ch/ into /e/ somehow or another complex mutation, but without finding the solution, we have just replaced one problem (p = k does not work due to lack of /pe/) with a new problem (p = ke does not work due to lack of /kech/).
Some further random thoughts and complexities- I do think that - to some extent - choice of glyph or indeed choice of word type is influenced by the amount of space available. I thought this was most likely at the left hand margin. This is relatively rigid and less forgiving of trying to squeeze a glyph outside it to avoid an unsightly clash. This may be behind the relative lack of some vertical pairs such as q-t and q-p, where you either need plenty of space such as a paragraph break or sufficient space between the lines to align the glyphs together...or you have the mess of the q descender slashing its way through the gallows' loops. The Vertical Impact work I presented at last Voynich Day, and the paper I'm doing now, goes more into this.
- I suspect that to some extent this behaviour occurs in the middle of the lines (e.g. if there is a long descender from the row above, this might influence a scribe to pick a word type without a tall glyph, or one where the tall glyph misses the descender) but this seems difficult to prove, since proximity of descenders to the taller glyphs is quite subjective and there are plenty of counterexamples including unsightly clashes. But my headcanon is that we don't often see words that have been split by the descender or large horizontal spaces between words to avoid this as much as we might expect. Descenders often sneakily and "luckily" tuck their way avoiding taller glyphs.
- I think the problem of the missing /pe/ is slightly overstated. This is because i) I think /p/ tends to occur in specific environments where Gallows-e and Gallows-a tend to be a little less favoured than say Gallows-ch or Gallows-o. And ii) more controversially, I have wondered if p tends to be added (or restored?) to initial ch words in the middle of the top row, thereby creating more of a bias for /pch/ than other clusters. That is still nowhere enough to account for the mysterious missing /pe/ but it's something.
- There may not be a suspicious quantity of missing /k/ in all top rows. Scribe 2 in Baleonological doesn't seem to be missing that many when you compare the middle of its top row to the middle of the rest of the lines below it. But then again, it is harder to feel confident about demarcating paragraphs in this quire.
- Both k and t do not behave the same in all positions in all scribes, despite having a lot of similarities. This adds a bit more complexity.
- P = k or ke doesn't help explain when /k/ is suspiciously absent in other positions where we don't see p either.
- Especially in light of the last point, I also agree about multiple word type variants and flexibility for scribes to choose (although their initial choice of letter may constrain them after that). The problem though is stopping this from making it unreadable to even the authorised reader. This obviously isn't a problem if the text is meaningless, although it is hard to then explain why a meaningless text would have complex rules that don't seem to correlate with available space.
If there is vacant space, I can say something hopefully more coherent on this on Voynich Day.