'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?'

In my circumstances, I would choose the latter. With the U.S. mortgage interest tax deduction (up to $750K I think for a couple), the effective rate might then adjust to a net of 5%. If BRK compounds at average rate of inflation + 8% or so, I'd much rather be invested in BRK purchased at an attractive price/ peak BV than to allocate a huge sum of cash to purchase a house. We are 6 years into a 30-year fixed 3.75% mortgage (put 20% down) and very pleased with this decision thus far.

The optionality is key to me, but my brother elected to completely pay off his house as peace of mind was his highest priority. If my memory serves me, even WEB stretched out his Laguna Beach house 30-year fixed mortgage payoff for nearly the entire term before he sold it.

Good luck and keep us posted as to your ultimate decision!