If you're a property owner who has been sued a dozen times or more, and all the other property owners you know have had similar experiences, and you've settled cases that you knew where baseless, just to save attorney fees, then this law will not likely make you more willing to allow climbing on your property. If you've had these types of experiences you will likely see no upside from allowing climbing and potentially huge downside. Even if the case if baseless and you get it thrown out by following Rodchester's arguments, you're looking at several thousand dollars down the drain. So, it doesn't matter if there are no climbing lawsuits - property owners will still not tend to feel comfortable allowing climbing on their property without real tort reform (a limit to the damages would be a great start).
Also, mattp - it's almost never just a slip and fall - usually, they try to make up some negligance or, even worse, discriminatory aspect to the case.
Most lawyers might be nice guys (not my experience), but the threat of massive damages from losing (however slight the odds) and the cost of legal fees make property owners highly risk averse. Sometimes you settle for a few thousand bucks, sometimes you fight and it costs you a quarter million dollars (when you win!), sometimes you settle for a lot just to avoid the hassle and risk....
Here's a best case scenario - I sold some property on Queen Anne and the buyer ran out of money on the remodel job, so their lawyer started sending my letters, "suggesting" that I might want to send them $10,000 to "settle" things. My lawyer basically told them to kiss off and that if they sent me any more such threats, that she'd have him disbarred. So, it all worked out well - except, it cost me $750 for three letters.