Only in places in the US with no sauna culture. Anyplace where folks actually have & use saunas in the US, it’s pronounced sow-na.
So back to the OP:
It’s interesting to note that most saunas you find in the US are not actually saunas, at least not in the “Scandanavian Sauna” sense. If the sauna is dry, it’s not a sauna. So I’m not going to really comment on the benefits of the sauna experience as it relates to the dry wooden boxes you see in hotels and such throughout the US.
So on to actual saunas. First, a description: a traditional Finnish/Scandanavian sauna is made of wood, with thick wood (preferably cedar) siding on the walls, and wooden benches. There’s a sauna stove, filled with rocks, and a source of water and a drain on the floor.
You turn the stove on, get it hot, and go in and sit on the benches. You fill a bucket with water, and use a ladle with water and dump it on the rocks to produce löyly - the heat and steam that surrounds you in the sauna. Really great traditional saunas have wood-fired stoves, but there’s more than a few electric sauna stoves that do a good job. The key, of course, is that they must be made to hold rocks & allow water to be thrown on them.
On to the benefits: there’s really nothing like a sauna that produces the deep relaxation that a sauna gives you. Indeed, I refrain from using mine (yes, we have one in the house) at times because it tends to mellow me to the point of sleepiness. Your pores open up, making your skin incredibly soft. Your muscles relax from the steam, and (if you stay in there long enough) you walk out feeling like you are a noodle, as good as a massage.
If you’re lucky enough to have a sauna where you can go in and out of the sauna into cool or cold air - or even better, into a snowbank - the hot/cold rush does something to your head. It’s an experience.
We have a traditional wood-fired sauna at our family’s cabin, 50+ years old. My home sauna is lined with cedar and has an electric stove made by a local-ish manufacturer who knows how to build traditional sauna stoves. I’d say a good 50-75% of the homes in my area have saunas; I rented student hovels that had saunas when I was in college. It’s a culture thing as much as a bathing thing.
For more sauna info, this is an excellent documentary.