The rent on a $500,000 property is $3000 a month? Maybe in some markets. But not where I live. I used to get $1700 a month for a condo assessed at $440,000.
And there are other benefits to renting. What’s the maintenance costs on that home? That’s an expense renters don’t have, and with some bad luck, it can be a big one.
This doesn’t invalidate your figures. But the truth is there is no one answer to the question of rent vs buy.