Open world shouldn't be forced in all games, even though nowdays you see open world games mostly in certain genres of games. I'm not going to go in-depth about this post, but I'm here to tell you a short story.
When I was younger, I was playing more racing games. They weren't as great as they are nowdays, but some of them had some kind of "open world"-type thing.. you could go off the main track and drive around the map, which was even more than grass. A part of the fun was skipping the whole racing and adventuring around the map.
It wasn't open world like it shouldn't be typically done, but it game extra value in the game as it wasn't only about being the fastest and the best. The adventure and exploration can give a deeper contact with the game, almost like a kind of a backstory. The world in the game can feel like it's so much more than the narrow viewpoint you get when playing.
However, going back to the post, the big wrong in open world games is forcing player to go around long distances looking for random objects. It's never fun. Most of the world should be an optional thing, not forcing players to run after petty items.
Is NFS Most Wanted on PS 2 was one of them? If it was, I had a lot of fun in that game too, messing around with the cops and driving around the entire city to find destructable constructions to crush them.
I didn't know if I was playing a racing game with open world-type of map, I didn't even know if it was called "open world". And I think the more we know about this type of game the higher the standard we put on this sub genre, expecting greater fun from games with this setting.
The shards collecting side quest I mentioned is the perfect example for your last statement. Well it's a side quest which means it doesn't force the players to complete it, but there is still "forcing the players to go miles away" part in it that we can see when we decide to go on that quest.
Nice profile pic btw, makes me hungry