But there's no way for the interruptor to know the priority of their issue relative to the your priorities.

This creates a major time management issue. If you have time blocked off for important, high value tasks, you can be easily distracted by someone else's lower level tasks.

Task switching, especially to focus on low level tasks, is highly inefficient in both the short and long term and should be avoided at most costs.

Sure, but isn’t that true in the remote world as well? I can’t imagine it’s very good form to just reject a call or ignore it when you’re busy doing something else, you have to provide a reply to the person about why you can’t talk, and then that’s just as good as having done the same thing to a person physically in your office.

I had a job where I telecommuted one day a week. On the days between, I helped people with problems, went to meetings, planned, etc. I could get a little code in every day, but any deep work would often have to be queued. I’d plot, scheme, research bug fixes and workarounds. Then on my remote day I would code like hell, all the stuff I’d planned out in the previous week.

On average, I got almost half of my code for the week done on that one day.

In my experience, ignoring someone stopping by your desk is very different from not answering the phone. A phone call doesn't have the same degree of immediacy nor the same expectations of a response

How is a phone call not the highest form of immediacy? Short of an actual pager event implying downtime and process, what could be higher priority to someone working out of office?

A voicemail. I frequently get calls, some of it may be a high priority, some of it not, no way to know, but I am not going to answer every call. If someone goes through the effort of leaving a voicemail I will interrupt my work and listen to it and decide whether or not it is more important than what I am currently doing.

I think it really depends on related context though. If I am working in an operational capacity then I may need to answer the phone every time it rings. If I am doing project work requiring a great degree of creative problem solving I am going to block off my calendar most of the day and prioritize a lack of distraction. My phone will be on "do not disturb" and I won't be looking at it. Impatience and interruption are the killers of creativity.

If you treat every inbound phone call as your highest/immediate priority, you have ceded all control of your priorities to other people. Unless you’re working in a call-center type of role, I can’t see how that could possibly be optimal.