My kitchen is vaulted just like the photo, with a skylight added in and it really opens up the space. Our Dining room has a center peak going from 9' to just under 12'. Playroom also has a center peak from 9' to 12'. I wish the family room ceiling was higher than 9' but we bought an existing house so not something we can change!

The issue with the "popular" 2-story rooms isn't the height of the walls, but that they are usually open to the foyer and second floor hallway or catwalk. That openness is what causes the major noise problems.

Consider which way the vault will bounce the sound in that room ... pretend it's a megaphone.

If the lower part of the area has a noise-producing activity such as a TV and the high part is aimed at your bedroom door, it's going to be bad. Figure out how and where to put the muffling objects.

You can help the acoustics, if not the noise level, with carefully hung textiles, bookcases, fabric upholstery, and rugs, but sound bounces. You can hang sound traps (fabric-covered panels) on the ceiling that can actually cut the noise levels, but you trade a dirt trap for lower noise.