First, in my case at least, it helps me remember things more clearly. If I read a book four years ago and didn't write a review of it, then I'd probably remember the general storyline, whether I liked it or not and that'd be about it. But if I read a book and then write a review of it, four years later I'll remember it much more clearly and, if I don't, skimming over my review will be a nice way to refresh my memory about the impression the book had on me. The same goes for anything else you could write a review of.
Second, it's an incentive to finish things. Maybe I'll be reading a really awful book and thinking of giving up. Well, I have a rule to only write a review if I get to the end of something, and if I don't finish it, I don't get the reward of writing a review! The same goes for hard or unfun games. "So, you just end up making yourself do things you don't enjoy?" I hear you ask. Well, no, that's not the case. If I push myself to keep going, I could well find later parts that I actually enjoy, but which I'd have missed out on if I'd given up (this is often the case).
My third and final point, is that if you make yourself write a review of everything you read/play/watch/listen to, then it gets you writing! This is only really a positive for people who are writers, but the more writing you do, the better you become, even if it's only a piece of non-fiction like a review. Plus, reviewing books might help you to identify negative aspects that some pieces of prose have, which you can then be conscious of in your own work.
So, start writing reviews! I'm sure there are people who would like to read them.
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