Today, I played my first "grinder". Just as 4th Ed. D&D borrows a lot from MMOPRGs, and LRF especially so, our local group has taken to borrowing the idea of "grinding through the lower levels": All of us have one character who we've focused on, who is our "main", and other who we've just sort of tinkered with (various "alts"). The Grinder game is all about leveling up the alts, by playing LFR games that everyone's been through already (as a player), so that we can crank through the RP and get to the fights... We did a game tonight (rated for 4 hours, the first time I played it it was more like 5.5 hours) in 2.5 hours. It was glorious.
And, it got me thinking more globally about the LFR concept broadly: the stories aren't very good (they seldom suck, but they're seldom something worth telling to my non-gamer but hyper-literate wife, either). But smashing monsters (and winning skill challenges) is fun. So, the 2.5 hour, abbreviated, tactical-tabletop-with-RP-elements game was actually great fun (even though I knew what we were about to face in every encounter).
Maybe, then, the goal should be to ALWAYS rock through LFR-- don't try to play up the RP-elements, but just let it be a series of tactical scenarios, loosely connected by a vague plotline that will, by and large, not connect to any other plotlines that any one of us will ever play.
If you want to play a story-driven game, find a good story-teller, and build a party. If you want to play a series of episodic one-offs, do LFR.