Why is it assumed that any space made by dying ash trees will be filled with non-native species? What evidence is there to support that rather than the idea that other native species will fill the gaps? What takes their place partly depends on what is around, plus several other variables.
Recently (autumn 2014) I cleared (hacked back) some of the Grey Sallow that grows in my garden. It was filling a space of about 60 square metres so that it was becoming impossible to access a corner of the garden. In the space I cleared these species appeared: Trailing St.John's-wort, Bifid Hemp-nettle (neither of these two, which are native species, had appeared in the garden before, but perhaps they blew in or perhaps their seeds were lying dormant and waiting for some space and light to thrive), foxglove, several species of moss, beech, rowan, holly, several species of mushroom, wild raspberry, and bramble. At least those are the ones I remember without going up there to check. oh wait! there were Himalayan Balsam seedlings too because there's some of that over the fence in the farm track beyond. I pulled those up, but even if I hadn't I doubt they would have smothered the young trees, whereas the native grey sallow did.
So, yes, non-native species might fill spaces left by dead trees but equally they might not. It depends on more variables than the appearance of some space where there wasn't before.
And besides, that's what happens in woods anyway! Trees die and new things, not always the same species, take their place.
I think a lot of people have a much more negative view of Nature (I include humanity in that word) than I have.