For straight crossings of the Alps, you have to get fairly high. Much of the terrain goes to 10-12k. The IFR airway MEAs tend to be FL140, with FL180 in some places.
A significant % of pilots fly without oxygen - both here and in the USA.
This was one celebrated example, with a post-landing pic
here. They don't like cannulas but, regardless of aircraft performance, they are flying with both hands tied behind their back.
BTW, why does pprune not allow certain URLs to be linked? It forces h t t p :// www. p run e. or g g in front of them.