Please note that US, Australia, Canada are English speaking countries. I find for a UK student to go to another country speaking his/her own language less adventurous and enriching.
The Erasmus+ extends also outside of the EU.
The UK could have brought in their relations with other universities and enlarge the network.
I've been also in Hong Kong with exchange students and there was a significant larger percentage of UK students.
There is an asymmetry here, these locations are quite attractive as its easy to make friends, the language is the same but the culture is slightly different, etc.
While Erasmus+ extends outside the EU the scope is really weak and lots of people want to go to the same places with limited slots, that is what the problem is imo. I can understand the attraction of visiting an English speaking country from another EU country but for an English speaking country it is still culturally enriching to visit another country where you are past the language barrier to go a bit deeper.
I think the more choices the better. I'm not against the UK having their own exchanges. I'm against the UK leaving the Erasmus program.
The UK already had exchanges programs to go to those countries that were not part of the Erasmus like Australia/Canada/Japan.
The problem is cutting the Erasmus.
Also in my experience students that wants to go abroad will go nevertheless the location.
When I applied for the Erasmus there was only 1 spot in the whole UK at the Glasgow University.
A student with better marks than me got that one. I got my second choice which was Bergen, Norway. It was the best time of life.
Leave the students the opportunity and let them know they have those opportunities
The Erasmus+ extends also outside of the EU. The UK could have brought in their relations with other universities and enlarge the network. I've been also in Hong Kong with exchange students and there was a significant larger percentage of UK students.