This is a really interesting topic and you made a lot of good points. I've been working on a massively multiplayer platformer for the last couple years (launching in a month!) that incorporates single-player style platforming while also allowing you to play with other players. As you mentioned, it focuses on platforming challenges rather puzzle mechanics.

The game is set up so players can join and leave the worlds at any time, so there isn't a separate mode for solo or group play. If you want to play with your friends all you have to do is jump into the same level. Players don't collide with each-other which allows for emphases to be on the platforming. Since players have their own screen they are able maintain their own progress in the levels and content isn't trivialized by using another player as a spawn point. The result is levels that are fun to play solo and become more exciting as people join in.

Many levels are designed so veteran players and new players can play together in the same world and enjoy the game at their own skill level. For example, a level might have several checkpoints that make it possible for a player to learn the level but it could make the level too easy for an experienced player. So levels can have multiple challenges that change how the level is played, such as adding a time limit, preventing checkpoints, or incorporating a more difficult path. This way if you are the first one to finish a level there is still engaging content you can play with your friends. This often adds a neat dynamic where you are constantly alongside your friends who might be stuck on a previous section, but have to take more risks when platforming due to increased difficulty.

So one solution you mentioned of creating more dependence between players could make an interesting game, I think also going in the other direction of removing dependence between players can also create engaging platforming you can play with your friends as well.