No, schools should not block websites.
Being a student, I think it's quite ridiculous that I can't use multiple educational websites because they are blocked. I have to do a lot of projects, most of which with videos. Because of the school's rules I cannot get onto YouTube to find a good video for my project. And come on, how many videos have you watched that AREN'T on YouTube? Very few, right? Imagine how hard it is for a student to find a video without these tools. Also, YouTube isn't allowed to have "bad" videos. Sure, some may be funny and not-school material. But 99% of the internet is. Soon, the only websites we're going to have left are the ones run by libraries. Try to find research on a LIBRARY site.