As usual, I agree with PheonixPhyre.
A huge part in multiplayer design is moving away from binary expectations. A player's mindstate is not "PLAYING" and "NOT PLAYING", it should always be somewhere between the two, that's how you make the player stay engaged. But having a system where every question is immediately answered with a Yes or a No (the DC system), and no rules about how to incorporate multiple characters or how they can interact with that roll, just makes it really, really poor for multiplayer. It's one of the many reason skills are terrible in 5e. Even the mechanics that slow the game down enough to interact with each other, like the Ready Action, are so weak that they aren't worth working together for outside of incredibly niche circumstances.
The complaints folks have about Martials is all based around those binary expectations. Trying to compare Anything to a Wizard's ability to Teleport just doesn't work. A Fighter can't get 80% of a teleport using his Fighter abilities, he either can teleport or he can't. His abilities are relevant, or they aren't. Breaking down those binary expectations, so that a player can always contribute using abilities that are relevant as dictated by the game creates a system where nobody is ever bored or irrelevant despite a lack of experience or creativity.
The problems of binary expectations are everywhere; try to eliminate them whenever you can and you'll find yourself becoming a better DM. For instance, instead of waiting for the player to come up with a reason why his 8 Charisma Barbarian should be the one to talk to the king, come up with a consistent way they can contribute that is still mechanically better than if they didn't, and now you've fixed more than just one scene.