I don't know why medieval homies built doors so short. They weren't short people. There's documented incidents of medieval kings accidentally dying from hitting their head on door lintels,
- "Charles died in 1498, two and a half years after his retreat from Italy, as the result of an accident. While on his way to watch a game of jeu de paume (real tennis) in Amboise he struck his head on the lintel of a door.[22]."
This surprised me, as I'd heard otherwise. Per https://www.sarahwoodbury.com/how-tall-are-you/, "the average height of people who lived in the 9-11th centuries was comparable to ours today. It then declined slightly during the 12th through 16th centuries, and hit an all-time low during the 17th and 18th centuries – when those doorframes were made."
A 2.5 inch difference in mean heights isn't enormous, and I think doesn't fully explain what the parent comment was surprised by—the merely 5'8" (173 cm) tall doorframes in the Fuggerei. Considering individual variations, something like a quarter of medieval adults should be outright taller than that.
https://en.wikipedia.org/wiki/Charles_VIII_of_France#Death
- "Charles died in 1498, two and a half years after his retreat from Italy, as the result of an accident. While on his way to watch a game of jeu de paume (real tennis) in Amboise he struck his head on the lintel of a door.[22]."