The idea of the side really has its origins in some of the early role playing games like Dungeons and Dragons. It seemed that you could not talk to anyone without somehow getting another quest added to your list. They were fun, but could get a little annoying when all you really wanted to do was get to your goal. In the end the side quest in an RPG game was used to build up your character for the challenges ahead. In your more typical first person shooter they can be used to do that, but also tend to be a little more fun. In some extreme cases the side quests are more fun than the game.
Recently while playing the game Dying Light I found myself stopped at 22% of the story, but I was finding as many side quests as I could. They were challenging and could get you killed, but the story line was getting boring so I found these more fun. I did not get back to the story until I ran out of quests to do. In asking around this seems to be a common thread in current games so I am not alone in this. It seems that much of the enjoyment of games like Dying Light are the side quests and opportunities as gamers look to do more than follow the obvious twists in the story.
Still there is a lingering worry about the side quest. Will these things become as annoying as they were in the original RPG games? Will developers find a way to make them evolve into something better and more engaging? It would be very cool if the side quest evolved into separate story arcs that let you get to the end of the game following different paths and even allow for the possibility of an entirely different outcome. Of course developers have to take two different types of gaming; multi-player and single player campaign, but that just adds to the fun.