It actually is not easy for invasive species to become established. They do have a hard time at first, before they become acclimated. A lot like us when we travel, in fact.
Of course, with invasive species, we don't want to give them the chance to acclimate in the first place.
The US isn’t the only place with an invasive fish problem. When I was in Japan, they were complaining about the bass and bluegills from the US. The bluegills were actually introduced by the emperor himself, and he apologized for that.