House purchase price might be easy to determine; although old records aren't always great; certainly the price paid indicated on the front of the deed is often a formal requirement value, not the actual price, so hopefully the real price was written down on the recorded deed too. I wouldn't rely on assessed values, at least without a lot of cross referencing many jurisdictions setup assessments so that they reflect market value, but jot directly.

On the other hand, cost basis in a house is not just the purchase price. Many improvements add to the cost basis, and good luck finding records to support that. Especially for a home owned by your parents since the 1970s.

That doesn't make it equitable to step-up on death; but it does make it very convenient.