arguably, the FOIA request cost the government as much money as the favicon, since these employees would have had to dig through old records to gather the information, as well as respond to the emails
As a 'victim' of a few FOIA requests, I can vouch for how much work goes into them. A favicon? Who cares when you've just involved 2 managers, a director and 4 mid-level federal officials? Some FOIA's were beyond reasonable and duly denied, but the reasonable ones could still take days.
Any costs incurred in responding to Freedom of Information requests are the price you pay for not being sufficiently open in the first place. If you pro-actively published everything that people are entitled to know (i.e. that you would have to release in response to a request), then these costs would be close to zero.
I can vouch for this as a former government worker. While FOIA is vital for transparency in government, there is usually quite a lot of man hours put into fulfilling these requests.
As a taxpayer, I'm quite happy to pay for this type of friction. Because the flip side of that is that government employees are constantly aware of the possibility of a FOIA request. I've no doubt it also places overall friction as everyone is constantly in CYA mode (I've worked in govt before) but even still I think the benefits outweigh the negatives. Even tax officials have to be polite to you, even if their objective is to extract a massive fine.
You are of course, correct (as ry0ohki states), but this one FOIA request could lead the way to more competitive favicon quotes from contractors in the future, leaving a net saving for HMG.
Sounds facetious, but it's this transparency that enables public scrutiny (and outrage). The expenses debacle being one such example.
I doubt that anyone, considering how much overhead there is in dealing with a government procurement process, charging anywhere like a reasonable hourly rate, could do it for significantly less.
Oh what, you wanted to be paid to attend that two hour meeting on diversity? Well sorry...