Not because it was clean. Because it was often the only private room: warm, with water already hot, away from a crowded cottage. A midwife heated it gently, for waiting. Sometimes a charmer walked three times around the sauna, against the sun, with a sharp scythe, to help the mother. It was dangerous: in 1816-1865, nearly one mother in a hundred died giving birth.

In the Kalevala, Marjatta asks for a sauna, is refused, and gives birth in a stable, where the horse's breath is like löyly. And where English Bibles say "the washing of regeneration", the first Finnish New Testament (Agricola, 1548) says "the löyly of rebirth".

Then hospitals came. But ask a Finn coming out of the sauna how he feels.

Was anyone in your family born in a sauna?

Sources: Living Heritage wiki (Saunominen); Sirpa Wrede in Maaseudun Tulevaisuus (2021); Hilkka Helsti in Yle (2010); Vau.fi on maternal mortality 1816-1865; Elias Lönnrot, Suomen kansan muinaisia loitsurunoja (1880); Kalevala, runo 50; Agricola's New Testament (1548), Titus 3:5, Kotus corpus.
Sounds: Freesound contributors, CC0.