You don't need to invest in the stat for this to work, to be clear. I agree that there isn't much benefit to doing a 100 intrigue run, other then just seeing what happens. But I am saying that there is benefit to investigating background, which is only going to be 1 turn of your run. Again, investigate background for Chapadoc + negotiate + personal quest ends up in a very fun set of circumstances.
I suppose that is 3 actions you have to invest to get her good, but it's not as if you can get her vote via cabinet slots, so I think it's worth checking out at least once.
One final thing: obviously you are entitled to your own opinion on how much you can connect to the characters. But as somebody who did recently replay LLTQ, I will say that the scenes in that game have very economical storytelling. The interactions between characters in it are pretty brief. If you're willing to play less efficiently, this game gives you a lot more opportunity to actually get to know the characters.