There’s no reason why sound quality should improve when peaks on the master are below -6dBFS as opposed to -1dBFS. None.
Not sure what you mean by that. There is no standard for digital to equal a particular level once converted to analog.
Mastering engineers don’t need peaks to be below -6dBFS for the purpose of having “headroom”. I’m willing to bet that in 99% of all mastering that’s done to at least popular music the track will be made louder, and the range between average and peak will be reduced. Because of this there’s really no need for headroom since generally the difference between peak and average won’t increase.
But even if that was the case the mastering engineer can easily solve any lack of headroom by simply lowering the track before processing. It takes about 1 second to do so and there is virtually zero loss in the process.