Would you say that "I wish" carries some sort of peremptory tone, or none at all? The difference being in the context of a presentation:
"I wish to introduce an idea" vs. "I would like to introduce an idea".
Which one would carry less hesitation?
I would say that "I wish to" may, depending on context, sound more curt, demanding and businesslike (in a word, peremptory) than "I would like to".
Consider:
"I wish to lodge a complaint."
against
"I would like to lodge a complaint."
Which sounds more natural? I think the first sounds a lot more natural to me. Since lodging a complaint is decidedly not a nicety, the phrase that goes with it is more fitting in the context of a demand or curt request.
However, in a more neutral or positive context (such as making a commendation) neither phrase comes across as more demanding, and both phrases would be appropriate. So it's not an absolute distinction.