Physical =/= mental. Mental is purely internal to the PC. Physical almost always involves external aspects which are generally beyond PC control.
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.
Fireball is external and generally beyond PC control and I the player generally cannot know for certain if he would succeed, fail or the outcome is in doubt. Anger is entirely internal and I the player generally know for certain if the PC would succeed, fail, or the outcome is in doubt.
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.
Taunts are not a threat. Nor can certain things ever anger me no matter who says it or how hard they try. For those things there could not possibly be any roll to anger me. Why should my PC be any different?
Because it is a game with many unknowns.
Putting aside sensitivities, one could codify emotional conditions.
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.
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.
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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.
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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.
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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