You articulated your point quite well, and somewhat convincingly, however, I find it misses the mark a bit. I could use the precise argument you did, to make the counterpoint to your assertion. Your almost convincing argument leaves out the most essential element to ranking and that is the hole in your logic.
PageRank on its own has no direct influence on ranking in SERP. Instead, it is used as a weighting factor on the influence inbound links have on your page’s relevancy score. And while your homepage could influence the ranking of internal pages, if properly linked, and internal pages may influence the ranking of your homepage, this does not occur unless you optimize your links for relevancy. The PR of the page is only important as a weighting factor of that influence on relevancy.
So while a properly optimized site may benefit from PR in the manner you described, you may also not benefit at all from that same PR if you do not craft your links in a manner that exploits the weighting potential the PR may have on relevancy scores. PR is not an important factor in ranking, relevancy is and PR without the proper application of relevancy is useless.
PR is only one of many factors that weight the influence of relevancy signals. It’s useful to recognize the most important signals of relevancy and understand the difference between those signals and factors that weight their influence.