Suppose a species is brought to another region, where it quickly overruns its
You ask a fair question and I suspect that some of the answer, in the case of the squirrels, is that the red squirrels are thought to be more attractive than the grey squirrels, so many people would prefer that the grey squirrels do not take over. But there are also reasons for environmental concern (i.e. not just aesthetic preference) in that there is reasonable fear of a loss of genetic diversity and also fear of upsetting the ecological balance. Invasive species cause the extinction of other species without replacing them with other new species, hence loss of genetic diversity (and vulnerability to future environmental challenges). Invasive species also often upset the ecological balance e.g. rabbits in Australia and then cause the extinction of several species, not only the species that they directly compete with. Grey squirrels are thought to damage the woodlands in England, and thereby the environment of some bird species.