Rules and restrictions
I've had the pleasure of working in education, small government, and companies that contract with the DOJ and DOD. I've personally been required and even advocated similarly dogmatic and overzealous measures over networks before.
It's absolutely true these filters are extremely inconvenient. Often requiring overhead to maintain as people in position X need a pinhole to access Y, Manager A wants website B locked down because people wasting time on it, etc.
Each company have different reasons this was necessary, but it usually boiled down to a mix of accessing things inappropriate at the work place, wasting time on websites that are of no benefit to work, and concern of malware from people who aren't cautious in their browsing.
I can say since most of these systems log who tried to access what when they got blocked it's both amazing and appalling the sorts of stuff people will do on the company dime. For us we usually turned the filter to just monitor to build a case to actually turn it on. I can say every single time we had people accessing porn, gambling sites, trolling around websites like rotton, somethingawful, and 4chan. Plus a variety of sites that deal in flash games, or otherwise have no redeeming value at work.
It improves company wide productivity
In my experience this has always resulted in an improvement in overall productivity. Even though individuals are effected by being able to access helpful tutorials on youtube, etc. Often the time people waste doing stuff they aren't supposed to be doing far exceeds that of the additional time incurred having to figure things out without these assets.
In a perfect world these filters would be unnecessary, but I can promise you everytime I've turned on a proxy to monitor traffic before going live it was staggering the things people would do on the company network.
Malware is just too dangerous
For a sophisticated user safe browsing is easy enough where it's pretty unlikely you'll get bitten by malware, the problem is most users don't know how to protect themselves from going to the wrong places and risking getting bitten by whatever the newest piece of malware is. Antivirus helps, but new zero day bugs come out daily and it only takes one virus to spread over your network to destroy any time benefit from not having the filters up.
I can say personally I've seen two companies get bit bad by malware. One was through going to places on the internet one should avoid at the office, the other was an infected USB key. Both cases cost the companies hundreds of thousands to millions of dollars as they were effectively shut down. IT had to take the network offline and go system to system cleaning the viruses off before putting them back on the network. One company this took the company of ~200 offline for almost 6 hours. the other it was effectively two full days.
Sure the filter can't fully prevent such a scenario, but it only takes one such occurrence to out weigh the benefit of having no filters.
Successful negotiation to be on the "lax filter" group
That said, in one of these companies we had a marketing department that the filters proved detrimental as some of the sites we really needed to filter from most people were the exact sites they needed to promote on.
They were able to come up with a list of about two dozen sites they needed access to in order to be effective. After some back and forth we decided to give them their own group. These filters are actually pretty good where sites are categorized by why they would be blocked porn, criminal, games, entertainment, malware, etc. What we did is for the marketing group we relaxed the rules a great deal, porn, malware, etc were still blocked, but we opened up categories that had sites on their list. (which actually was only opening up two groups of something like 18)
Turning off the filters entirely was just deemed too dangerous. Not to mention as I said before overall productivity improved despite the impact caused by some useful sites getting blocked.
I know someone will probably go. "I would never work for this sort of company" or "They probably have high turn over" the first is by all means your choice, but I can say we didn't see a notable impact in employee retention from before / after we put filters in place.