Narrative Guy says, "Some of the best games I've ever played didn't involve a single die roll; we decided what our characters could do and the GM took us through a story."
System Mechanic says, "That's not gaming. If you don't have a mechanic, then the characters are subject to the capricious whims of the GM. And how can you make sure everyone is on the same page? Also, you lack the random element." So...what do you think? Make your case!
If a rpg is to have something like a competition of skills where you play skills you don't have, then you need a system mechanic. Otherwise, you tend to get a echo set of the skills the Players do have. The guy who knows martial arts will somehow seem more martial-ly. The social chatter will someone seem more charming.
However, since each Player and their GM is a 'random element' in themselves, I don't think you have to have dice or cards or coin-tosses to make a system mechanic work. There are some very interesting games out there now that work on 'bids' of resources, or poker hands, or pools of dice that escalate conflict.
All that being said, I prefer to move as close to Narrative as possible, leaving system to be some trick of the narrative or a simple scale that all can keep in their head without reference to books or charts.
If I'm going to refer to notes or data in game, I'd like it to be something directly supporting the story. Better still if I don't have to do any of that.
sidenote: Why does MT sometimes make hash out of punctuation in quoting other blogs? I get that from Ginger and Li. Macs? Why would MT fumble Mac text? I get quotes and apostrophes translated to number sets which do not display right at all.