There is a reason why the Germans called it the “Widow Maker.”
However, IIRC the F-104 was the first jet that had a thrust to weight ratio in vertical mode greater than 1. A rocket, essentially.
If I recall the story about the German ones, there was a problem with the pilot oxygen that was eventually traced to the company that supplied them. Seemed the intake for the supply was too near some kind of exhaust. Just what I remember, don’t know if it’s true, but you can search for “post hole digger and starfighter” and “widow maker” and see for yourself.
Never heard about the O2 problem, by the 80’s I suspect the problem was fixed.