Please do not flame me if you are a Sony fanboy and believe differently. This is just my opinion, and quite frankly I don't find waiting 20 minutes to play my damn game fun..
Here's a video from RoosterTeeth explaining:
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I got this game and not only was the download ridiculously slow, it also froze during installing trophies so I had to restart the console. Ended up with corrupted data so i had to reinstall.