Gosh, buying an index with home equity makes a lot of sense. Because as we all recall from 2006-2009, the stock market and the housing market never crash together.
Duh.
What happened in 2006-2009 was an outlier in the history of home ownership. I know. I had heated arguments with family to convince them NOT to buy a home and had almost damaged valuable relationships if not for a crash. Besides, what happened was extreme leverage and concentration in the same asset.
Now take that outlier away and you are simply matching the best liability (h.e.) with the best asset (equities) available to people. It's Capital Budgeting 101. Obviously moderation is in order. And if you can produce reliable Sharpe ratios or predictable drawdowns, then it's time to back the truck up (at the start of a business cycle).