I was too busy to post this last night, but here is some anecdata I have gathered over 15 years of coordinating Erasmus exchanges between a French university and around 10-15 (numbers have fluctuated over the years) UK universities.
We have certainly had non-UK EU students (German, Italian, Spanish, Czech, Polish, Slovak, IIRC) who were studying at a UK university come to France on the Erasmus programme. All of them have been notably motivated and hard-working, as well as linguistically agile, which cannot always be said of our incoming UK Erasmus students. (Anecdata, again, of course, which will rightly be washed away in a flood of cut&poo.)
We had around 100 incoming students/year, more like 60 since the Brexit referendum, and have never had more than 3 or 4 non-UK EU citizens/year. Many years we had none.
We have never, in 15 years, had a French student come to France on Erasmus.
Why the hell, if they have gone through the process of settling in the UK to study and can get financial aid and access to study programmes in another country, would they then mooch back to France?
It's an interesting insight into anyone's mindset that they would even think that, TBH. A bit like the notion that those getting benefits are all "scroungers."
Most students who go on Erasmus exchanges are by definition open-minded and keen to discover new places and learn new languages, not looking for a cheap way to spend a semester somewhere they already know.
Suggesting that it doesn't matter that tens of thousands of UK students will not benefit from international mobility because some non-UK students have also benefited in the past is... well, I can't find the word.
I could google and c&p one, maybe.