I think it’s more complicated than this.
I can only discuss my own region, but some species that are undergoing range expansion due to climate change may be marked as introduced - but they are not invasive or dangerous.
Some people plant pecans, persimmons, osage orange, dogwood, baldcypress, magnolias, gingko, redwood, medlar, tecojote, pawpaw, the list goes on and on - in places where they don’t grow on their own and can be considered introduced. They are not dangerous.
Some plants from Europe, like dandelions, are marked as introduced but others, like stinging nettle, are not. Daffodils and peonies come up for a hundred years in the same place and don’t spread here - they are often useful markers of old house sites.
Chicory might be a horrible noxious weed elsewhere in places where it’s introduced but here it’s just a chill summer plant that hangs out at the side of the road. If city government tackles it with herbicide, it gets replaced by roundup-resistant pigweed, which is a new problem for evil big ag farmers now, and in part drives the reformulation of pesticides.
Some introduced species, like domesticated corn and ducks, are the byproduct of human activity and not likely to flourish on their own. Peregrine falcons in Illinois have been described to me as “frankenstein’s monster” in terms of their reintroduction genetics and could possibly be considered introduced.
The microorganisms in your body are introduced from every place you go and food that you eat. Definitely not a cause for alarm.
Some species here, like common earthworms and chinese mantids, are so prevalent and widespread that there’s not much anyone can do about them to restore “balance.” It’s true, and it’s tragic, but it’s not something we can fix. We pour endless amounts of chemicals and time and money into restoring tiny fragmented parcels of land, and maybe even a few big ones, and protecting ones that seem to be healthy, but the damage was honestly done when people started (insert your favorite: agriculture/colonialism/cars/ships/plastic/global commerce/existing/something I haven’t thought of).
You have to prioritize what is a cause for alarm.