It's a power game. Presumably less Americans visit places that require visas since there are enough places that don't. So Americans may not want to go to Europe as much. Currently plenty of European tourists go to America, so maybe that doesn't bother them as much. Pick a third world country like Jamaica. Americans can go there visa free, and Jamaica wants Americans to continue to come, so it stays visa free. However Jamaicans require Visas to go to the US, because the US had decided that it doesn't need to encourage Jamaicans to come to the US, enough already do.

Maybe someone could analyze from 2009-2010 data, did the introduction of ESTA have any effect on how much Europeans traveled to the US.

Americans have many destination options, including America. Any barrier is going to reduce the number somewhat

Presumably it also means some number of Americans are going to be legally prevented from entering Europe when they wouldn't have had any trouble under the old system.

Yeah, it's just hyperventilating. If I'm spending five-digit sums of money on a trip to Europe, an extra $10-20 per person for some electronic nonsense is not going to stop the trip. It's a hassle, sure, but a pretty small one.