You are conflating two things:
1. the loss of most of our hair
2. the evolution of what hair we have left, and why we didn't go entirely bald etc.
You seem to be saying that because a theory to explain 1 isn't about the sensory function of hair that this means that they're arguing against the sensory function importance for 2. That isn't the case at all.
And you seem to be assuming ectoparasite avoidance - which sensory sensitivity would enhance - could/would have no role in the initial evolving of furlessness. And assuming incremental change rather than abrupt - that there was ongoing hair loss headed towards true hairlessness, that had to stop for the hairs to gain another role. I think you are assuming the order changes happened in.
They're not competing against each other, but theories for 1 and 2 can run in parallel. So please stop thinking that they're in competition.
I've said already ectoparasite and thermoregulation hypotheses are not in competition. As well as possibly evolving in parallel (or independently) the different elements - hair size, follicle nerve supply, eccrine glands - can also evolve sequentially. Getting the hot weather endurance need not be the immediate benefit, but a benefit that emerged later with subsequent evolution of sweatiness and that reinforced the success of the furless hominid and prevented a reversion. As sensory sensitivity could have evolved later. I don't know, but neither does anyone else, not even biologists specialising in evolutionary anthropology. All possibilities deserve and arguably
require consideration. Unless we can bypass the surmising and hypothesising and we end up being able to read our evolutionary history from our DNA.
Given what anatomy tells us - that we have evolved exceptional sensory sensitivity - it seems like that
matters, or else requires showing that it has no relevance to evolving furlessness. That has
not been done.
I don't know which order - no-one does - and we don't even know if the changes (or which aspects of hair size, follicle nerves, eccrine glands) could have been abrupt or which, if any might have or must have evolved incrementally. Abrupt mutational changes to developmental genetics could see spandrel-like combinations, including I would suppose, furlessness plus increased sweatiness or all of them together or combinations of them.
Incremental evolution? Given what we see - a developmental trait that is primarily and universally expressed in the pre-pubescent young, who appear to be retaining infantile furlessness (small hairs not growing larger on time, not loss of hairs) until puberty - and that
furless childhood is universal and shows no apparent differentiation across the entire species, no matter how varied the post-puberty, secondary sexual hairiness. We don't see evidence of incremental change to that development, just to post-puberty traits. And the assumption that loss of hair in humans remains ongoing - that we are becoming
more hairless - is one more unsupported assumption that remains popular.
Furlessness alone can give
immediate benefits with respect to fur borne parasites and parasite borne disease - differences in disease susceptibility can be a powerful and
fast natural selector, changing the balance of a population potentially within a single generation. It would work better with enhanced sensitivity but would not require it.
But furlessness alone won't give thermoregulatory advantage - and appears to give significant thermoregulatory disadvantage for
children. Not without the significant change to eccrine glands as well.
The enduring absence of due consideration for a sensory function that enhances parasite detection is something I can't see as anything but scientific negligence, a failure of basic observation. And subsequent to Montagna's anatomical observations - 1985 onwards - a failure of basic academic research.
Body hair in modern humans serves no useful purpose was the enduring assumption (that still persists), reinforced by persistent absence of recognising the very existence of the principle function human hairs demonstrably have. It is an assumption that is readily observable to be false.
Darwin
might have been capable of recognising hot weather endurance as an advantage of "nakedness" and therefore changed his view that furlessness could not have arisen from natural selection, but it was a failure of fundamental observation to not notice the sensory function of hair, which observation would also lead to the possibility that our furlessness evolved out of natural selection.