In what reality is PMI close to a rent payment? It doesn't seem like you know what you're talking about.
I think you're dramatically overestimating how much it will add to a mortgage to use this strategy. For example, let's look at a $250,000 home - the average for my area.
If you put 20% down, your payment will be $1242/mo plus Property Taxes. Certainly cheaper than rent, but most folks don't have $50,000 sitting around.
So let's say you put $0 down and roll $9000 closing costs into your mortgage. Your monthly payment will be $1,843 of which only $214 is PMI. Still cheaper than the average rent in my area.
Even if you're buying a $1mil home with this strategy, the PMI would only be $850/mo. Where are you getting that PMI would be close to a mortgage payment?? You seem to be regurgitating bad faith advice that keeps people scared of homeownership when the reality is that it's an excellent move for many folks.