Assuming these fax machines are being used instead of PCs then one could imagine a worker being less productive than they otherwise would be.
[1] https://www.economist.com/britain/2017/11/09/what-fax-machin...
Trying to think of examples where I've seen this, the first thing that comes to mind is receptionists in my dentist's office. 2 or 3 surly, over-makeup'd women sat around chatting and occasionally dealing with customers. Maybe a good starting point would be to fire 1 of them and pay the other two more (or more likely, use the higher pay offer to get better people). Of course what really happens is that the business keeps that money and doesn't hire new/better employees, making the current ones even more surly but no more productive.
Going down this rabbit hole I conclude it is a cultural problem, but every solution I can think of (better safety net and higher minimum wage to push these people out of the workforce, for example) feel like they would be inordinately expensive.
The missing puzzle piece for me when trying to better understand this topic is what "productivity" really means. I get the notion of "output per unit of work" - but there is never much attempt to peer deeper and understand why productivity is lower here.
Is there actual evidence of workers doing less on a given day? What does that even look like, for example in the retail sector where workers seem to have very little impact on the purchasing decisions of customers.
If it isn't employees, where does the lower productivity come from - are we just outcompeted on cost because we still try to have too much of a low-skill economy which can't keep prices as low as the developing world? It would be good to compare productivity in the UK with countries in Scandinavia, i.e. those with a better social safety net and without the financial centre of gravity that is London. Where does their productivity come from?
These are the kinds of topics I'd like both journalists and politicians to discuss more - but for as long as they have to cater to the lowest common attention span, I'm not getting my hopes up.