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.