You would need to improve the railway.
Hull is where the new trains have been ordered for because there aren’t enough existing ones. Even though it’s a major port, the line isn’t electrified (which is ridiculous - the whole Liverpool - Hull corridor needs to be electrified) so rather than electrified Intercities, the line is getting smaller, slower battery operated trains (very much the second class option).
The NE local train service is inadequate as the line capacity is taken up by intercity services on the mainline. The Northumberland Line is more frequent & has been really successful- but again the trains need more carriages.
West Yorkshire & Manchester are better but even here services could be improved. I think Manchester wants a metro/underground service to bridge the gap between trams & rail. Leeds has wanted trams for decades.
As I said earlier on this thread, if a student can get to an intercity service, then they will have the choices you mention. But if they are on a local line / or need a bus journey to get to the station then that will inevitably reduce choice. Driving also has its problems due to congestion in major urban centres (this can mean it takes a long time to travel short distances due to stop-start traffic and it also means that it’s undesirable to add large numbers of students to the existing commuting traffic).
I also think if there was to be a move towards students staying at home, then for fairness there would need to be some benchmarking between universities & some grouping of unis so it would be accepted that a degree from any university in a group is equivalent. That would mean that you would have to accept that degrees from Manchester, Durham, Leeds etc are the exact equivalent of Oxbridge. That wouldn’t necessarily be a bad thing, but it would be a massive shift in attitude & seems unlikely.
Without this, then higher education is going to increasingly become unfair as fees & living costs increase, as students living close to a university or those with parents able to support them living away will become increasingly privileged.
There was a MN thread last year on this when there was a BBC (I think) article about a Manchester student living at home - it was very quickly pointed out on the thread that that student was very fortunate to have a good public transport link to one of the best departments for her chosen subject. That really seems to sum up this issue.