Here's your error: you're assuming the mortgage will never be paid off. Which just isn't true.

not every single one makes money.

You know what corporations do with a property that doesn't make money? Either they find a way to kick out the current residents to raise rent. If that is not possible they sell. A corporation doesn't give a shit about you still living in the building before selling.

they buy the house outright and don’t pay a mortgage on it.

you very apparently have no idea how property development works. Those companies have at any point in time almost no cash on hand and while they might pay a good chunk of a building out of pocket credit is usually still the way they go. There are very few companies that don't need credit for daily operations, in property development that number is even smaller because their daily operations include paying for construction basically all the time. Even if they were paying out of pocket the difference would be interest, not some magical 33% as you suggest.

580,000 4k a month

Not sure what you are smoking but with a 25 year mortgage my calculator says that's ~2k a month (without interest). Now interest will add some to that but not 100%. Unless you are getting a loan from a meth dealer in a back alley. Without any upfront payment some random mortgage calculator spits out 2.4k per month on that property for me. We can talk about the math when you come back with numbers that add up. Going with the numbers of your closing sentence anyway here's some math for you: Rent: 2.8k / month House: 3k + 1k + 1k (1k repairs, 1k upkeep. Repair from earlier mentioned 20k/2years, upkeep from home owner annectodes around here estimated upwards)

25 years: Rent: 840k House: 1500

40 years (25 + 15): Rent: 1344k House: 1860k

50 years (25 + 25): Rent: 1680k House: 2100k

in which case yes, you are absolutely right. But that would also be the point at which I question how you arrive at a 4k or even just 3k 25 year mortgage for a ~600k property. To me that means either your bank is ripping you off or your credit history is so low the bank doesn't even think you can afford your next breakfast. That level of difference isn't even at a point where I can chalk it up to difference in interest rates. The number you gave me initially (4k) would be a 100% total interest rate. Again, I don't see how that works out.

If your mortgage numbers are correct then you are probably also correct in that the owner would be running a loss on the property (a steep one at that) assuming they are still paying a mortgage on it.