In a lot of ways it depends on the purpose. I could totally understand if Chris Lord Alge didn't want interns, co-workers, producers, and bands in and out of his house 24-7. Based on the sheer volume of work the major studios have, it could become quite unmanageable. It'd never be quiet enough to relax with your family or get some sleep.
However, if you take studios like the ones Kid Rock, Will Smith, Bon Jovi, and Dave Grohl have, which are commercially equipped private production spots, then that becomes a non-issue.
As far as an advantage of knowing where everything is at, but there are also a couple of variables. You'll know your own studio, but when someone else comes over to mix in it, they won't. And there's a good amount of guys that never really learn how to use their stuff, and they have to hire someone to come over to setup and track for them. For example, I seriously doubt Witney Houston, Michael Jordan, and Will Smith actually know (or knew) how to use their own tracking rooms.
I think what it comes down to is that its different for 3 different groups: Orchestral tracking studios, mix studios, and cinematic sound studios. Non-Orchestral music tracking facilities roughly fall into the same camp as the mix studios, where they're benefiting more
For the guys like Tom Lord Alge, who have moved into their own houses and ARE mix engineers themselves, then certainly. If they're comfortable, and they trust the acoustics of their own rooms I would think the privacy issues could be dealt with by simply controlling their client bases.