What evidence is currently known that favors or disfavors the hypothesis that a regular beat of some kind—that is, an “isochrony”—plays some important role in languages?
I've run across some claims that there are three main ways that languages have regular beats:
an equal time per syllable,
an equal time between stresses,
and an equal time per mora (a beat that takes less time than a syllable, where a typical syllable takes a small-integer number of morae: one, two, or three).
On that hypothesis, different languages or different speakers may depend on different "isochronies" to different degrees, but people rely on some kind of isochrony for comprehension of most or perhaps all languages. My question is: what evidence is there about whether this hypothesis is true—do (many) languages depend on some sort of regular beat at the same order of magnitude as the length of a word or syllable?
I am not asking whether languages can be unambiguously categorized as stress-timed, syllable-timed, or mora-timed. This question is about whether a hypothesized mechanism of language exists, not about "typology". If isochrony exists, it might have multiple forms, which might or might not provide a basis for defining categories into which some languages could fit, but I'm not asking about ways to categorize languages. I'm including this paragraph because nearly all the writing about isochrony that I've found so far is arguments about whether languages can be unambiguously categorized in this manner—which is not what I'm interested in. It's OK with me if plenty of languages make use of two or three (or more) isochronies simultaneously. I just want to know if isochrony really matters at all.
Some information I've found so far
One argument that different kinds of isochrony exist is that the variance in syllable lengths is greater in English, which supposedly depends more on regular stress-to-stress intervals, than in Spanish, which supposedly depends more on regular syllable-to-syllable intervals. However, as Mark Liberman says in this blog post (which is mostly about the categorization argument), that doesn't imply anything about isochrony, because syllables in English have a much greater range of complexity than syllables in Spanish (due to the variety of consonant clusters that English allows before and after the vowel). Liberman says that people have been trying for a long time to save the isochrony hypothesis by postulating various ways to measure the assumed regularity (for examples, runs of successive syllables of the same length), and claims that no one has ever found an objective measure in the sound of speech itself. I don't know if that's true, though.
A weird argument is that the perception of isochrony disagrees with the timings actually found in the sound signal, and that people adjust the real timings of syllables and stresses to create the perception of isochrony. There must be some interesting evidence for or against this, but I haven't found it yet.
This paper by Peter Roach attacks the categorization theory, but also has a note from the author saying that it's out of date.
So, what evidence is up to date?