If you are a low-level programmer or work for a very small startup yes, but at scale communication and coordination overhead is necessary and significant.
As a tech lead I am keenly aware of the tension between the fact that interruptions may shoot my technical work to hell, but if it helps 10 other people be twice as productive that day it might well be worth it to sacrifice my own productivity, especially if the interruption is of the "teach a man to fish" variety.
So be glad your interruptions have a net value. Maybe my anecdata is untypical - It would be nice to think so.
OP says "there is something wrong with the business world where you have to avoid the interruptions of the 9-5 to get things done"
I reply "even if nothing is wrong, the needs of others can conflict with the need for focus"
Then you reply "but most interruptions are not necessary for anybody's productivity".
That has nothing to do with my point. I'm not diagnosing the work world in general. I'm saying even if you fix all the problems, there will still necessarily be distractions in the 9-5 that an engineer might seek to avoid.
I am saying that a legitimate work environment where everything is relatively sane and people are respectful can still be tremendously distracting when you need heads down time.
Higgs is of 'Higgs Boson' fame and recent Nobel laureate :)
I would think that if you got up at 4am you could get your work finished in less time (say by noon). Unless your job relied on communicating with other people during working hours (9-5) that seems feasible to me.
I want to make two comments - firstly there is something very wrong with the business world when you have to avoid the 9-5 full of interruptions to get any work done. I know this from experience.
Secondly compare this to the Peter Higgs (of Bosun fame) saying he would never have got an academic post today because he would not be seen as productive enough - in other words he did not get up at 4 to do a days work before going and doing a days interruptions.
We are getting something terribly terribly wrong with our working days.