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In a prior company, back in the days when internet BW was much scarcer than it is now, my IT guys wanted all the restrictions you mentioned above, and I said "no". Instead I told them to make a list of the BW sucker sites and apps based on actual, instrumented measurements of usage. Then I sent an email memo to every employee ASKING everyone to be aware that careful use of those things during the core biz hours would help everyone. It was very effective at optimizing our BW usage, by making everyone aware of the problem and part of the solution, rather than making everyone feel like they were being punished.
Local caching is also a good idea, but it needs NOT be user specific. If you survey the traffic you will often find that many people in the company are looking at the same content (biz related or not often because links are being emailed about. Cache that silly cat playing the piano video locally and the BW hit is negligible .