For what it's worth, at 2.675% interest on a 30-year fixed, buying a house in cash makes very little sense, and a mortgage can counterintuitively
earn you money.
1. In general, since the 1970s, house prices have across the United States tracked inflation. The price per square foot on a house, on average, is exactly the same as it was back then (houses are more expensive because the average US house has gotten bigger, and in some metros like SF, city councils have flatly refused to allow building to buff up house prices).
2. A mortgage is basically free when you discount inflation and deduct the interest. The fed target for in the US is roughly 2%. This means that a 2% interest mortgage is free money, i.e. while you pay a 2% interest rate, the principal is worth 2% less, as you get to pay off the 2020 house price using 2021 dollars. So a 2.675% APR mortgage has an effective cost of 0.675%.
3. If you're working you get to deduct the entire 2.675% (of the first $750,000 in mortgage), so you get back up to 45% of it if you're in the top tax bracket. As such, the effective interest rate discounting inflation and interest tax deduction is negative, -0.53% APR.
4. On top of the interest rate on a 30-year fixed being effectively negative (i.e. generating value), you can invest the other 80% of $450,000. You should have no trouble generating 7% per year on that $360,000.
5. In aggregate, your return on capital by making a 20% down-payment on a $450,000 house at 2.675% APR in the top tax bracket could easily be ((0.53% + 7%) * $360,000) per year, plus your house should appreciate in value at inflation, but because it's a 5X leveraged investment, you're generating (2% * $450,000) per year on a $90,000 down-payment.
So, your total return could be:
1. $90,000 @ 10% + $360,000 @ 7.53% or...
2. $450,000 @ 2%.
Given the lack of fees or penalties for pre-payment, you can always pull the ripcord if your situation no longer makes sense by just paying it off.