Which is a personal opinion and anecdote, but the courts are very much out on this, as are others. Whether or not it encourages reckless cycling is impossible to quantify given the lack of data pre-Strava, but it's certainly the opinion of enough pundits, bystanders, those involved in incidents, that it may have encouraged more reckless behaviour.
I think it's one of those things that given enough time, we'll have more of a clue. But certainly whilst we can't say it does, we also can't say it doesn't.
Going back a few hours to the Strava questions. It is probably true that we do not yet have enough data to prove that Strava encourages more reckless behaviour.
What Strava does do is to encourage people to go faster [I don't do Strava so tell me if I have got this wrong]. Going faster doesn't necessarily increase the risk of crashing, I doubt if it would decrease that risk.
It seems very likely that the physical/medical consequences or any crash are likely to increase with speed. Where a crash involves hitting a solid body the consequences are likely to increase with the force of impact which increases with the square of speed.
So if you go twice as fast and crash the force of impact will be four times higher. Or with Strava you are encouraged to go 10% faster the force of impact will be 21% higher. That is enough to change a minor injury into a major one, or a major injury into a fatality.