A better solution would be to charge for making a reservation, and give that charge back as a credit against the meal. You don't have to raise prices, you increase the probability that someone making a reservation intends to show up, and when you have a no-show, you get compensated for the empty table (and can still give it to a walk-in.)
Restaurants like State Bird are a bit of a poor example, anyway. Regardless of their reservation book they're going to fill all their tables every night anyway right now, and they don't particularly want larger (5+) parties anyway because they're tiny. I think they want prices low enough that they can establish a loyal clientele that will keep them going once they're no longer the "hot spot" in SF. Or maybe (gasp) they like offering their food to a broader range of customers. Chefs tend to be a little more down-to-earth.
Feel like if they market this move a little better, they could convince their loyal customers that this will allow them a better chance at getting reservations.