Basically that's the way I've been doing it for decades, although I found out that a quarter inch of water is enough.

Physics tells us that the six minutes work only at or close to sea level. At higher altitude, water boils at a lower temperature, so the cooking time must be increased. For instance, in our vacation home in the Swiss Alps at about 1400 m (4600 ft) above sea level, eggs of a normal size need around 6' 40", and really big ones need slightly more than 7 minutes.

Physics also tells us that the eggs won't cook faster in steam, because the temperature is the same. However, you save quite a bit of energy because the water will reach boiling temperature much quicker. Maybe that gave you the impression that the cooking is faster.