There's not as much crossover as you might think. In North America the native pollinators are adapted to the native plants and can't even pollinate the introduced eurasian ones. And it goes the other way: honeybees can't pollinate the native plants, only the introduced eurasian ones.

If course, if you're in Europe, honeybees are the native pollinators. At least around the Mediterranean.

While I haven't done an intense study of it, I very frequently see multiple bee species, natives and honey bees, on the same flowers. This includes things like raspberries, mint, dandelions, various fruit blossoms, as well as vegetables. I'm sure there is specialization in at least some of the natives, but some of them, the bumblebees especially (or maybe that's just because they are bigger and easier to see), seem to be pretty generalist foragers much like the honey bees

So, what you're saying is that honeybees are facilitating the spread of invasive plants in North America? Seems like a definite negative.

Those ships have literally sailed, centuries ago.

https://en.wikipedia.org/wiki/Columbian_exchange

Invasives are an ongoing and escalating problem.

Which is solid evidence that honey bees have little to do with the problem.

See also earthworms facilitating spread of invasives:

  Invasive species of earthworms from the suborder Lumbricina have been 
  expanding their range in North America. . . . Their introduction to North 
  America has had marked effects on the nutrient cycles and soil profiles in 
  temperate forests. . . . Some species of trees and other plants may be 
  incapable of surviving such changes in available nutrients. This change in 
  the plant diversity in turn affects other organisms and often leads to 
  increased invasions of other exotic species as well as overall forest 
  decline. They are considered one of the most invasive animals in the 
  Midwestern United States along with feral swine.
https://en.wikipedia.org/wiki/Invasive_earthworms_of_North_A...

We also have many wild bees in Europe.