WFH can also greatly increase productivity.

Can != does

Exactly.

So, to rewrite your prior message:

WFH does reduce commute time.

WFH can (sometime) reduce productivity.

Well, WFH can be good or bad depending on how is done, on both sides, worker side and company side. I'm an EU home worker and I have experienced some issues on my sides and many on company sides, that's much a matter of knowledge and willingness to test and improve.

Most managers, at least in EU, can't really get WFH, not just in terms of synchronicity or asynchronicity but in mere practical terms: they simply fail to understand the "job" part vs the "office boilerplate" part. This is an enormous issue that might reduce productivity alone. Most workers fear the change so tend to have poor home office setup and that's as well can lower productivity.

All these phenomenon are not part of WFH paradigm but just part of an evolutionary path we have all to do to understand. It's not much different than the old UK rule to put a horse in front of any train to control their speed. Now, do you prefer to have forever a horse in front of every train or having get rid of them is a good riddance?

WFH can save both employees and companies money IF done properly, similarly working on site can save money and work well or not, it's not a matter of where you work but how much you understand how to work in a certain way or another. The whole society can save money and live far better if the society evolve well, and we still have absurd procedures with pdf forms made not as forms but as to-be-printed, then scanned, than mailed tools, because those who have designed such procedure do not know nor understand the "modern" world (modern quoted since pdf fillable forms, digital signatures, web forms etc are modern, but definitively not new).

Now try to project the cost for a company of:

- eliminating offices, so not rent, cleaning services, electricity, ...

- enlarging they potential employees choice at least at a national level, if not the entire world (witch might be fiscally complicated)

- being able to move their fiscal residence as they want since there is no physical boundary

Does companies save money with such model? DEFINITIVELY YES, at least if they know how to do, and their best interest is trying, learning from errors, correct them and keep evolving instead of bovinely hold untenable positions just because they know them and fear the change.

As an employee I do save money WFH, but to do so I've invested much, I left a big city for mountains, building a new home and so on. I've studied and have done the change. A company can do the same with LESS investments typically.

In our company the _measured_ productivity is higher since we WFH.

Not convinced that productivity can be measured for most SWE work.

It is sort of measurable. How many lines you output, how many bugs are in your code, how much time is spent fixing your bugs. Etc. I mean its far from perfect and leadership roles are harder to measure (but can be measured by how the people under them think about them). But still I get your point.

I think the best we can do is have an expert familiar with the task and codebase evaluate contributions. Trouble is, this can be corrupted by all sorts of internal politicking.

People have been trying to measure productivity for many years. If you found a good method you should publish it.

We still do Agile Scrum, and our velocity has gone up significantly. Experienced team, mature code base, no real external forces to skew these figures.

Goodhart's Law does not apply, as we have done this for many years and are happy [1] with the way we do things.

[1] for some value of happy