Something to keep in mind is that once you own a few rentals, it's easy to pull equity out for a down payment on another rental, and buy the rest with a loan. Leveraging is easy when there you are buying physical assets that retain value.
In other words, even if you own 10 rentals, you are probably wealthy, but the bank my still own a majority % of those assets.
The goal is not to own the rentals, the goal is to own the cashflow through the control of the properties (whether that's mortgages, leases, or option agreements with the owner). To your point, you want to be stripping equity whenever possible to accelerate asset acquisition. Very similar to private equity LBO operations.
If you're highly levered (as a smaller landlord), and funneling that income into retirement accounts protected from creditors (varies by state for IRAs, 401ks are federally protected), it's all upside with no downside. Heads, you walk away with appreciated real estate you eventually cash out of. Tails, you walk away from your investment properties while your retirement assets are protected with credit blemishes that are quickly forgotten by lenders. It is rare to be pursued by lenders in recourse states, as being (mostly) judgement proof and the option of bankruptcy are significant hurdles.
Home equity loans or cash out refinances. What you pick is determined by your financial models based on interest rates, origination fees, etc. Typical carrying cost math.
Once you have enough properties to bump up against Fannie or Freddie GSE underwriting guideline limits (~10 properties), you transition into commercial lending, where you build a relationship with a bank and they lend against your combined portfolio.
In other words, even if you own 10 rentals, you are probably wealthy, but the bank my still own a majority % of those assets.