From a roleplayining perspective there are many good reasons for investing solely in the intimidation skill and not persuasion. Underrail is a RPG after all.
And I'm ok with, not every dialogue have both a Persuasion and an Intimidate option for solving an issue with non-violence. It's just that, when I see a dialogue option incorporating a skill, I expect that by choosing that option, the game will check my skill and I will be successful or not.
I kind of liked the it was handled in Fallout: New Vegas, where you got the skill requirement for succeeding before you chose that option.
To clarify, if the aforementioned intimidate skill check in the mindreader showdown is higher than 100, I find it a bit unreasonable and if it is a skill check that is not meant to succeed, there shouldn't be an option to use intimidate at all. It's at best misleading and set the player up for failure where there is no hope for success.