Yes, one of the key benefits of working at home is control of the environment, and that most assuredly includes who gets to interrupt, or not, and when.
Working in company offices, I did some pretty good work. I tried hard, despite being very uncomfortable and unhappy. That was the job. But working at home, I did great work, became financially independent and most definitely happy. I loved (still do) my office and would (still do) burn huge numbers of hours in (t)here really Getting Shit Done. I also established myself in a very low cost-of-living location, doing high pay-in-employment work. Remotely. That's a really nice side effect of remote work, or at least it was for me. Hearing about real estate expenses in areas like Silicon Valley and various similar enclaves, I can only shake my head at the difference. I spent less in total (under $100k, all told) on nearly 6,000 sq feet of totally custom (and admittedly very eclectic) environment than most of the people in those areas spend on one bedroom apartments in less than 4 years ($2300/mo.) It really matters to your quality of life where you put your roots down.
TBH, I think one of the most programmer-hostile things a company can do is say "you have to work where we are." The tech exists, and has for some time, to make that completely unnecessary. Even if "constantly interrupt and monitor" is part of the company's operations protocols, that too is 100% doable. Throw the employee a fast connection and a good desktop, a webcam and a mic... whatever you need to do to keep in touch, you can do. Should cost a metric fuckton less than providing them office space "at" the company, too. I have never, ever, heard a decent argument for the requirement that warm flesh be present in the room in order to get good work done, or out of any employee. Frankly, if the employee can't work like that and do good work, they sure as **** aren't doing great work for you in any bloody office.
But, you know. I'm old, cranky, successful, independent, and can say these things with no fear my supervisor will see them. :)