If you could, would you rather pay cash for a house or invest that cash in Berkshire and get a ~6.7% 30-year fixed-rated mortgage?

This is such a personal decision and goes well beyond the math and tax calculations. I suggest you get really introspective about this if its what you're considering.

Now what I'd do--- I'd put 20% down like most Americans and try to find myself a good deal in the market I'm looking in, I'd buy the school system if I had young kids, I might get a little fixer upper, I'd look for some inexpensive ways to improve the value (maybe a new kitchen or a new bathroom, etc.) Also, buying new construction can be a great deal as there will be no maintenance needed in the first 10 years or so. Then I'd let inflation take the value higher(3-5% inflation is really good when you're a homeowner leveraged 5 to 1). I'd want a really affordable payment, I'd also look to refinance at a lower rate in the next few years. Maybe I'd try to pay it off in 10-15 years, but not right away.

With the remaining 80% I'd probably put 20% of it in an emergency fund at a bank and then I'd layer into Berkshire with the rest when I thought prices were low. And I'd add to it and read these pages to figure out how to build a portfolio.

For another perspective, Morgan Housel wrote in his book "The Psychology of Money" that he paid off his home. It helps him sleep at night knowing that no matter what happens in the markets his home is paid for.

Other things to consider: Your investing temperament, stage of career, other assets available, other large expenses in the near term and job security.

Hope this helps.

Best,
Chris