I believe you meant emotional rather than mental.
A DM can ask you to solve a puzzle or recall something and have you roll INT checks.
Insight is a mental skill.
So, you believe physical and mental (as defined above by me) challenges are roleplaying and a game. Emotional challenges are roleplaying solely.
How you do you account for the Madness and Sanity mechanic.
Not quite. While insight is mental, it's not guaranteed. That said, I often as a player decide if my PC divines some insight from the actions and words of an NPC without any roll at all. I can be right or wrong, just like a roll. When I do roll for insight, it's more often an attempt to confirm my thoughts than to come up with new information.
I say mental, because I decide what my character thinks and believes, not the dice, and those things are mental.
Madness and Sanity mechanics involve the supernatural. They aren't a bear in the woods.
In fact, it is very likely a particular PC is going to attempt a Persuasion check at the 4th Council (ToD campaign) to try sway certain leaders to commit to the fight against Tiamat, and he will likely be reminded, rather harshly, by critics how he failed his party (he is the last remaining OG of the party, others are new) and arguing as to why should the Factions put their trust in him when he cannot keep those closest to him safe. i.e. they will goad him.
To let the player decide without any input from the game seems meh. Why would you let a player get away with roleplaying that nothing happens to him emotionally EVER. i.e. Always immune.
Why would you play with a player like that? I don't. If someone is at my game to just game the system and not really roleplay out a PC with personality and character, they should find a different game to play in. My game is not the one for them.
One of my players had a character who had a serious phobia of the undead. He was terrified of them when they showed up, often running or hiding. Sometimes he would overcome it a bit after a few rounds and try something long distance. When an undead that caused fear showed up and he was asked to roll a save for his character he said, "No. I fail that roll automatically. There's no way I could overcome supernatural fear in my state." So he ran his behind off for the duration of the fear.
So this is how I envision it:
Stakes will likely be set and I would lean heavily on his bonds* (related to the party and a certain OG PC).
PC will make an impassioned plea for commitment by the Councillors.
NPC councillor will antagonise him.
PC will need to make a WIS (willpower) saving throw.
- Success he holds the line and makes a straight Persuasion check gaining a +1 modifier with 2 councillors on the scoresheet, with an additional councillor affected for every 5 above the DC needed.
- Failure, frustration gets the better of him and hurts his position, i.e. Persuasion at Disadvantage, but gains a +1 modifier with one councillor on the scoresheet.
- Critical Failure (Failure by 5+), character must make a Sanity save.
(a) Success - he holds back an angry rant or tears (player chooses). No modifiers gained on scoresheet.
(b) Failure - his emotion (player chooses) takes hold and sees him unable to converse momentarily like the Madness condition for mundane effects and is penalised a -1 modifier with 2 councillors on the score sheet).
As DM I can offer the player 1XP to impose a disadvantage on 1 check or save in the scene by leaning into one of the character's bonds. Player may decline.
The player can offer a disadvantage on one of the rolls for 1XP by leaning into an appropriate TIBF. DM must accept.
*Actual character bonds
- Keep the party together
- Protect Aidan (OG party member, now NPC and descending on his ace into Avernus (BG: DiA campaign)).
EDITs: For clarity
I'm not sure if it plays out like that, or if you've just organized it for understanding, but if it plays out like that, I'd hate it. I like my social encounters to be smoother than that. I want to roleplay back and forth, occasionally stopping to roll some check or other and then the social encounter moves on from there with the direction dependent on what the result of that check was.
I'd hate to have to stop and figure out what the PC will do, what the NPC will do, and what the stakes are before starting to roleplay.