Good point.  Naturally-occurring assemblages of plant and animal species evolve together, striving to eat and not be eaten, until over the course of thousands or millions of years a sustainable balance of numbers is achieved to where prey doesn't increase to the point of exhausting its food supply and predators don't eliminate all their prey and then starve.

Invasive species haven't gone through this process when introduced into a novel system, and therefore disrupt it.  Sometimes catastrophically.  The more invasive species you introduce, the longer it takes the system to reestablish equilibrium, and the more extinctions result.

Different introduced species will have different effects--some perhaps minimal, some anything but.  Example, introduce northern pike (Esox lucius) into a stream where they didn't naturally occur and you end up with no more native salmonids and nothing but a stream full of stunted pike--and a few really big ones--with nothing to eat but each other.