I'm not entirely sure what the point of Erasmus was, especially from the perspective of UK students, because the arrangement is you pay what you would've paid anyway.

As such Erasmus was/is a real stitch-up for British students because our uni fees are stupidly high. I went to uni in 2006, so paid >3k. In my halls was a French guy who came to study for a year. You still pay the fees you ordinarily would, so he paid like €300. Had I wanted to study a year in France I'd have been no better off. The situation is worse now fees are even more ridiculous.

I'm not seeing what benefit that confers over whatever (if any - they may just apply and be accepted like anyone else for all I know) scheme attracts, for example, Chinese or Indian students.