Personally I see a few Co-Op games, but most of them tend to make bad decisions on how to make the story work while either playing alone or playing with someone.
in some cases they find a quite good balance between Co-Op and Single player being on the same story but this usually is rare to find. Either they make Co-Op to intrusive or they split the Co-Op too much that you barely notice that you are playing with another person. There is also the fact of single player where the AI might be "dumb as bread" and is completely useless or doesn't even partake in lets say 'boss' fights in a meaningful way.
There is one workaround which would make it work flawlessly and that is having two separate storylines one made for multiple people and one made for one person although this would probably increase development time quite noticably and thus not valued from a company's perspective.
Another issue in some Co-Op games is the Co-Op campaign where the story, rarely give the same immersion as a single player story would, even more noticed is tendencies to being too simple or overly complex making you feel like, "ahh, god I have to help my friend ontop of this ledge again to make him open the door for me" every other 5 minutes.