I can vouch for using oxygen at those kind of altitudes, if you are older.
A few years ago, when I was the same age as Churchill in 1944, I ferried a glider tow plane for three hours in the Canadian Rockies. Two hours between 9,000’ and 10,000’, following a highway and then one hour above 10,000’, going “over the rocks”.
After I landed, I felt very disoriented, it took me a long time to do the unloading and re-fueling, and although it was a good landing, I couldn’t remember if I had put the flaps down!
I realized I was hypoxic. Now I always use oxygen when going above 8,000’, which in a glider, means it is simpler to be on oxygen for the whole flight. It has an added benefit of making me less tired, which is good for decision making during a long flight.