Unfortunately this is a pretty good example of misunderstanding major vs secondary market forces. Key word major, since the rest of your points are correct, just not as correct, with the exception of your point on limited supply, which is also a major driver.
When you have super-low interest rates, you can pay a higher sticker price on the house per equivalent dollar of mortgage payment. Therefore the price of the house can rise to the point of people bearing the mortgage payment. This affects everyone, and creates bidding wars because the sticker price of the home doesn't actually matter; the cashflow effect absolutely does.
In the case of PE entering the market, that's a secondary effect of low interest rates. PE operates pretty exclusively on leverage, so without super low rates they wouldn't be entering the market because it wouldn't be as profitable.
You might also say that boomers' homes being underutilized is actually a secondary effect of the major driver of limited supply. If boomers have to consider the option of moving into a smaller place like a condo (which may be less price-stable compared to a detached home due to condos being more commodified), or an assisted living / seniors community (which likely has a higher cashflow impact than keeping their paid-off home), then why bother making any change at all?
TL;DR - the government needs to get back in the housing development game; we need to maintain a higher interest rate environment (as distasteful as that might sound to some); and what we really need is immediate blanket rezoning for aggressive densification (like Calgary city council is currently attempting).
Also fun fact: the Conservatives support none of those things, so, y'know, consider that when voting in a few short years.
THIS RIGHT FUCKIN HERE