On the mechanics side of things, I had issue with how Intimidation interacts with the normalized Influence rules.
First, there's the old issue with tying Intimidation to Charisma. In some senses it works, but in others it really doesn't.
The other Charisma skills — Deception, Persuasion, and Performance — work very much in a positive correlation with the expectations of Charisma. Being charismatic makes people more inclined to like you, believe you, and enjoy being around you. It's easier to convince them to do things your way, they're more likely to say good things about you to others (increasing your reputation), and so forth.
Intimidation is the exact opposite. It's about getting people to fear you. Any reputation to be gained is in you being someone that people don't cross. People don't like you, and don't want to believe your lies. Certainly you're not putting on an entertaining performance on stage.
This is a longstanding complaint about the Intimidation skill, of course. Some suggest changing the stat used to Strength, to be better suited for the brutish fighter types who presumably would be more likely to use sheer presence to influence people in this way.
I actually don't think Strength is a good match. I think, instead, that Wisdom is the best stat to tie to Intimidation. Wisdom is already connected with the Animal Handling and Insight skills, both of which feel like a much closer match to the act of intimidating someone — reading someone's state of mind, and carefully shifting it at a primal/emotional level.
Of course, this suggests clerics and druids might be some of the best at intimidation. And, well... a priest giving a fiery speech about hell and brimstone seems pretty intimidating to me, as would a grubby woodsman who might turn into a bear and tear my head off at any moment. So I'd actually be fine with that. Certainly more so than bards or sorcerers or warlocks trying to be intimidating. And Wisdom isn't a complete dump stat for warrior types, so as long as they take proficiency in it, it works at an OK level for them, too.
However that's only covering the first half of the problem with Influence. The other (major) problem is that the latest playtest gives you advantage on influencing Friendly creatures, and disadvantage on influencing Hostile creatures. For Persuasion, Deception, and Animal Handling, that makes sense. For Intimidation, though, it feels completely backwards. You're not going to use Intimidation on a Friendly creature, and while you'll want to use it on a Hostile creature, now you're at disadvantage? That's nuts.
Honestly, trying to tie any advantage/disadvantage to the Friendly/Neutral/Hostile axis just doesn't make sense for Intimidate. If anything, I'd say you might get advantage/disadvantage based on size and numbers. If you're larger than the creature (or have a trait like Powerful Build that gives you an effective boost to size), or you sufficiently outnumber the target, you can get advantage. If you're smaller or have fewer numbers, you get disadvantage.
I commented on the feedback that I thought this was a problem, but didn't have solid thoughts on how to fix it (or the space to write in something like this).
