And maybe use int/cha/str for those checks, depending on the approach...There is definitely a lot of possible overlap between Deception, Intimidation, and Persuasion. I mean, often isn't Deception really just trying to Persuade someone you are telling the truth? In many ways you could roll them all up into one skill: Influence, because that is what you are really trying to do IMO 9 out of 10 times.
Regardless of how you try to influence someone in a social setting (lying, intimidating, etc.) if you fail in the effort, there will be consequences (of course, this is why an ability check was called for...). Intimidating isn't alone in this.
Which, again, is a matter of interpretation. When someone whose character is trained in Persuasion makes the rousing speech to get the townsfolk inspired to take on the bandits and they think they're being their most persuasive self but the DM then calls for an intimation check, that just leads to annoyance.Making intimidation "I seem impressive" works great.
Persuasion - "Be a good chap and listen to this deal"
Deception - "This lie is true, clearly"
Intimidation - "I'm an impressive person, you should show deference"
One way to use Intimidation is a threat, but far from the only one. Getting people to charge the goblins because you are so badass that together you have a hope is intimidation. Getting people to charge the goblins because it is the only way to save their town is persuasion. Getting people to charge the goblins because the goblins have diamonds is deception.
DM: "The thread claws its way out of the ground and faces you."Looks like someone cast Animate Thread. Such net-cromancy is a dark art, of questionable provenance!