The student loan system allows more people from every social class to go to university and join the middle class. Loan repayments are linked to income after graduation so nobody has to pay back more than they can afford.
Your "and join the middle class" step isn't happening. There are two classes of people who graduate from college at this point.
The first graduate with degrees and skills that are useful - or can be made useful - in the professional world and start working immediately.
The second graduate with degrees that are useful for the sole purpose of teaching others those exact same topics and nothing else. They get paid a fraction of what the first group is.
While we need some teachers, professors, etc, the low pay in these roles point at an overabundance. If there were less people seeking those roles, recruiting them would become a priority and pay would rise. As we're seeing in software development every day.
You know what works even better to up the system to people from diverse backgrounds? Direct payment of tuition costs by the government. It's well documented that the rising tuition has reduced access for people from lower income families. Students have no power to negotiate tuition costs with the politically entrenched adminstrative class. Politicians, on the other hand, would have the power and career training for that kind of negotiation.
In the UK increases in tuition fees (by up to 3x) has had no effect on the diversity of university applicants. This is because repayments are income linked (and have an income floor) so that a graduate on a low income makes no repayments at all. Only those who earn a large salary will make significant repayments.
If tuition is funded by the government then this will force those without a university education to subsidise those who do go to university. Also university places would have to be limited to control costs.
suggest there was a slight increase in the percentage of lower-middle and working class students in 2012/13, but this was set against a drop in total UK student numbers of around 6%.
Those are the most recent numbers I can find. They don't break out the details.
>If tuition is funded by the government then this will force those without a university education to subsidise those who do go to university.
There's absolutely no reason why this would have to be true. There are plenty of other possible income sources, not least a much less tolerant attitude to off-shore tax avoidance, raised property taxes and the removal of loopholes that support tax-exempt foreign trusts, and taxes on quick-flip investment speculation.
The UK is actually swimming in cash. It's just not very evenly distributed.