I would disagree with you on the pedantry. There would be two separate transactions: a buy buys the property from the seller, and the borrower borrows from the lender.
The property is treated as collateral, but the buyer/lender is the owner of the property. Mortgages are a bit special different from most common consumer debt because of the timing- the transactions need to be simultaneous because you need to have the collateral to get the money, and you need the money to get the property, but afterwards you still have ownership of the property.
Whether it’s a mortgage, a car, putting a latte on your credit card, or a multi-billion dollar corporate acquisition it’s the same.
That aside, the rest of your comment I agree is good advice to consider, but it’s just part of the equation. You’re assuming the mortgage is actioned as plan throughout it’s lifetime. However, the borrower has options. They might want to pay early and will save a lot of interest that way (maybe more than just interest if they have PMI). There’s also the option to refinance out of a higher rate later on.
Also… You’re comparing two different things by asking if a house listed for $300,000 is worth $700,000. In order to do a fair comparison, you need to do the same calculation for every house you consider and for the entire market you’re basing your expectations around. The only houses worth $300,000 when you factor in the interest of a 30 year mortgage would be a fraction of that cost. Or if you’re comparing to the alternative of not buying, then what you really need to compare is the cost of renting vs the interest you expect to save in whatever period you expect to defer buying for.
