Raising prices is the wrong way to address this behavior. Ultimately the restaurant wants to maximize yield, not just average meal price. Open tables are wasted inventory. So the priority should be to stop bots from grabbing reservations for people who aren't that committed to eating at the restaurant (and thereby stealing them from people who would actually go dine.)
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.
On the flip side, I made my first reservation through opentable a few weeks ago, and I was surprised when they DIDN'T ask for any cc info. Granted I was new to the experience, but the first thing that crossed my mind was I could not show up and it wouldn't be a big deal.
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.
Only very popular restaurants require a CC on OpenTable. One of the nice things about OT is that it's very easy to cancel (one click) which I suspect also helps restaurants maximize their yield, since they don't have to keep a table open for a reservation that never shows up. Taking a CC may discourage some people from making a reservation so if you're not already at capacity, it may not be a good play.