Of course it's a workable system. Do you think they just arbitrarily came up with some numbers without doing any modelling? Why would they want to introduce a system they already want to change? How does that make sense?
Yes, that's what they do all the time - that the sums quite obviously don't add up at this stage should raise a big red warning flag*. If you want to make an unpopular change then you don't just make it, you nudge people and get them used to the idea first. When I went to university the idea of paying for your education was unthinkable, so they nudged us toward the idea of student loans - first to replace the maintenance grant, then for small tuition fees. Now they want students to take on huge debts, well they need some way of saying "it won't be that bad, you'll pay less than you do at the moment despite education being more expensive". Then a couple of years down the line, "sorry guys, too many people aren't paying their loans off - we need to make a few small modifications to ensure everyone pays their debts in full".
It's like when they wanted to introduce road charging, let's take a busy section of motorway, build a relief road and charge people a small amount of money to get them used to it. The result was the M6 toll, opened in 2003 with a perfectly reasonable charge of £2 for a car. Seven years later, the charge is £5 - the business was simply non viable with the initial charge, they had to raise the prices but if we had been told it was going to cost £5 in the first place the M6 toll would never have been built as the opposition would have been stronger.
It's not really taking on any debt in any normal sense of the word. It's simply a graduate tax with an end stop of either what you owe (which relates directly to your course) or 30 years.
Debt is debt however you look at it. If it wasn't a big deal the government wouldn't be keen to push the debt off its books and onto students.
* Edit - the government have already been caught out once with this and been forced to include a concession guaranteeing that the £21k a year threshold will rise in line with inflation for the next five years.