It depends.
On a strict financial basis Martin Lewis is probably your man. However most people don’t make spending decisions, on anything, based solely on the basis of an accountant’s advice. (My accountant wishes they would. He regularly tells clients they can’t afford to divorce.)
Behavioural economics comes into play. How much do value:
a) money now versus money later, ie your personal IRR. (This assumes you have the money now.)
b) what satisfaction would you gain from having your DC start life debt free. For some it is a case of wanting their DC to have the same as they did.
c) how do you view the state and state funding. Some people prefer that the state has the money to spend on other pressing social priorities, and prefer to go it alone. Others see it as something their DC are entitled to, so not an issue.
And so on.
On the economic/Martin Lewis front, a lot depends on likely future earnings. Even ML suggests the answer is not clear cut for medics. There is also attitude to risk - who are these loans going to be sold onto. What happens then. I have also spotted a divide between Londoners and others, with the former aware that if a young person wants to survive in London, they are probably going to need every last penny of income, like their parents did, and the deposit for a house can wait till the parents sell up.
Also importantly, it depends on your DC and how reliable they are with money. We pay. We also drive a 14 year old car which won’t be replaced until DC have finished University. We were also planning a staycation this summer. (We are still planning a staycation!). And we can wait another year of two before doing up our house - we have already waited 20. DC know this and have been careful with the money we give them. Indeed they get less than others from less wealthy backgrounds, and have still been able to find the money to replace phones and computers, go on trips to visit friends abroad etc. If they were likely to be spending it, and more on drink —or drugs— we would have been less interested.
So for us it is a win. DC know the value of money because they know where it comes from. They are likely to be highish earners anyway. And we get the satisfaction of them entering into the adult world debt free. I also like us operating as a multi-generational unit, who support each other. We have the money, and this is how we choose to spend it.
So no right answer. Your money. Your priorities.