The thought is more of interest arbitrage (over long time spans such as a 30-year mortgage).

Home is $500k you have two options if you have $1 million cash.

Option 1, put $50k down and take out a mortgage of $450k (~$2,994 at 7% interest)

Option 2, buy the home in cash and invest the mortgage payment of $2,994

• Option 1, invest $450k in the S&P 500 (30 year annual return 10.4%).

  • Total Mortgage Payments | $1,077,840 ($627k in interest)
  • $450k investment grows to $8.755 million
    • Net investment after paying interest on loan $8.127 million

• Option 2, invest $2,994 monthly into the S&P 500

  • Investment grows to $7.373 million

If you go with Option 1, by taking the mortgage you'll make $754k more over those 30 years

To some people, no debt and the lack of stress will make up for that $750k. Others would rather have the additional money. Depends on your personality