On first glance one would think the rule limiting the pitcher to two throws to a base would have an effect. But I disagree, in most cases.
For 95% of base stealers the runner is only going to attempt a steal on a specific count. Usually this is when the pitcher is ahead in the count, say 0-2, or 1-2, sometimes 1-1. The reason is the pitcher, when in a favourable count, can throw a waste pitch, trying to get the batter to strikeout on (usually) a breaking pitch out of the zone. There is no reason to throw a fastball for a strike in these situations. The team at bat know this and figure a slower, breaking pitch in the dirt is a great opportunity to steal.
However, the half dozen players per league with elite speed can go on just about ball-strike count, including fastball counts (2-0, 2-1, 3-1.) These are the guys that pitchers will use the pick off move and throw over to the base to keep the speedsters from taking that extra step. In other words, the speedsters are going to run, better hold them on base by throwing over.
Pitchers don't use the pick off move on guys with decent speed too often. They will throw over if there's a speedster on base but he's going to steal no matter what. This hasn't changed with the rule changes.