I see. I completely misunderstood. Thank you for the clarification.
For retirement purposes, it is my opinion (and I want to stress the opinion part), that you cannot include the equity in a rental as part of your retirement savings. The reason is that, without either selling or taking out a loan against that equity, you cannot use the equity to draw 4% from each year. In order for that equity to actually provide any value, you would need to use a reverse mortgage, take out a home equity loan, refinance, or sell the house. Selling the house would mean that you don’t have any rental income, and any of the loan options would likely offset most of the rental income.
IMO, using your case study, Bob has either $10k/yr in passive income from a rental, or Bob has $500k in retirement savings from selling the rental, but I do not see how Bob would have both. However, if Bob needs $20k/yr to live on and expects to use a 4% withdrawal rate, then by selling the rental and netting $500k, Bob will be able to meet the $20k/yr requirement.