Can definitely see that being an issue. I know a lot more people that stayed in Liverpool after uni than with people that went to other places though.
There's a large Irish student population and a good number of those seem to stay.
A big part of Liverpool is the nightlife, and I know of a lot of student run (or originally student run) electronic music nights (way more than in Manc for example). That kind of thing contributes a lot to the city, entertainment-wise, socially, and economically. I know students aren't famed for spending much but most of what they do spend is on nights out, and these events aren't just aimed at students anyway.
I think the youthfulness keeps the place vibrant and moving.
Another big plus is that it's quite a concentrated city centre, which makes getting around pretty easy.
I feel wrong praising the city in this thread.
Who exactly were you playing? Uni of is very middle class, JMU team didn't have loads of scousers when I was there, (no) Hope might've done, there's LIPA which is performing arts, and then Edge Hill which I can't imagine being rough.