What is 'meaningful'? It has the potential to change the outcome of a lot of encounters. Personally, I always find it extremely important to play my *characters* 'right': not having any points in persuasion can ruin the experience, even though I can, mechanically, play through the game without any issues.
For example, my Sebille is not really running for the next Nobel Prize, so she has no aspirations to achieve world peace (tm) by being an expert diplomat. But there are occasions where it really matters to me that she passes a check, e.g. when she threatens somebody to obtain information. I find it very frustrating when that bombs; it should not really matter if Sebille, a professional assassin and interrogation expert, recently sweet-talked Attila the Hun into having a tea party. Having her whisper into your ear while she pushes the tip of her dagger into the skin of your neck will surely provide adequate motivation to keep her happy, no?
Speaking of which, I have not really understood how those [WITS] or [STRENGTH] checks come into play in combination with persuasion skill levels. My experience is that almost all checks have failed when diplomacy was low, i.e. even high attribute values did not make a difference. Conversely, almost all checks have succeeded when diplomacy was high, i.e. even abysmal attribute scores lead to a successful skill check. Seems a bit one-sided to me, but ultimately that is a good thing, imo, because I sometimes find the way they match attributes to diplomatic approaches counter-intuitive at best; I'd prefer a simple tonal choice in those situations, really. E.g.:
"No, I won't tell you who stole that ring."
[INT] *You point out that stealing should not be tolerated because it would erode society standards and order in general, and ultimately lead to nobody being safe, including him. He would really be helping himself by helping you.*
[STR] *You pick him up by the throat and threaten to smash his teeth in if he does not reveal what he knows.*
[CON] *You point out that you have a lot of time on your hands, and that he'll have you camping in his living room for the next few days, unless he tells you what you want to know.*
While thematically, all options make some sense with the way they are matched to attributes, a peaceful and patient character with low CON (e.g. the wizard-archetype) would fail the [CON] check required for the peaceful and patient solution. Similarly, my Sebille would prefer something like the [STR] check, as discussed above, but bomb the check because she has absolutely no STR, all DEX (err... finesse, of course >.>)
TL;DR: I find persuasion extremely important for the role-playing aspect of the game, but recognise that the implementation of it often leaves a lot to be desired. I don't even know how it should be implemented in an ideal world, perhaps this is simply a limitation of RPG systems in general.
Personally, I usually cheat to obtain a high persuasion skill in RPGs like this, so I have free reign to pick persuasion options when they are required to stay in-character. The benefit, for me, far outweighs the slight loss of 'challenge' presented by character specialisation.