To a degree, they sometimes are. Every plant or seed catalog I have ever seen has had at least one plant they’re selling that is considered invasive in some part of the US. And the listing doesn’t always warn people, so they may not know they’re buying something invasive. Especially if it goes by multiple names.
As an example, one of my favorite seed companies that specializes in medicinal herbs, often has Alehoof seeds in their catalog. It’s a useful herb and a good groundcover. It’s also known as Creeping Charlie, the bane of lawns and gardens in my area. Once it gets a foothold, you can never get rid of it!
For that matter, some of the medicinal herbs I’ve had trouble getting established, are actually considered noxious weeds in their home territories.
That’s not even getting into the problem of contaminated soil, or infested lumber that is often sold for landscaping purposes.
So, it makes sense that nurseries are a factor in the spread of invasive species. You can debate how big a factor they might be, but to say they don’t play a part at all is not logical.
We raised wheat seed to use for planting. I bought foundation seed and produced Registered seed for my crop 2 years out. Then planted registered seed and produced certified seed.
We have a seed cleaning and treating plant. So each year we carefully clean the seed drills, the combine (we own one, don’t rely on custom harvesters for our planting seed crop at any stage), and the seed cleaner. Normally we only grow a single variety at a time to make the clean up complete. Including the seed cleaner itself.
Then there are the purity and germ lab testing that is done for each plot that is required in order for them to sell me certified seed tags. (and registered)
I know about planting seed purity issues.