I agree cake. No amortisation schedule here, but a memory of how broke we were with two young children and a new London mortgage. Loan repayments on top would have been the final straw. Hence the instinctive desire to pay costs up front.
In addition there is the issue of independence. As parents you do your best to raise and educate DC. After that it is up to them what they do with their lives.
Paying till they graduate and then letting them launch seems simpler than then dangling the incentive (?) of a house deposit over them. Will there be conditions attached. What if one DC is in a position to take on a mortgage, and the other is not? What if you really don’t like their partner or other life choices? What if, as it typical in London, the house buying has to wait until you are established in a career? I know DH would have felt awkward taking money from his parents when he was in his 30s.
The further London wrinkle is that DC tend to boomerang. They may not want to return home, but London is often a good place to launch a career, the City is what they are used to, and the cost of renting is such that a childhood bedroom starts to become more attractive. If DC return to London, their deposit will have to come from a combination of saving on rent, saving on not repaying student loans, possible inheritance from grandparents, and for some, money available from parents downsizing. As a parent I have a very selfish interest in my children, and future grandchildren, being able to afford to live in London.
(On the other thorny subject of adult children paying rent, we would probably take the approach of not charging if we knew they were saving.)
Again, though the decision may be informed by financial predictions, there are a whole load of personal, behavioural factors to take on board. Plus lots of unknowns. Will the massive current Government borrowing effectively be paid for by rampant inflation? If so Martin Lewis might well revise his figure to suggest paying up front rather than 9% of earning into the foreseeable future, will be a better investment for a wider group. Will a future mum find the prospect of loan repayments, on top of child care, commuting and other employment costs, acts as a disincentive to returning to work, going full time, seeking a promotion, or adding to pension contributions. Paying up front means you never have to think/worry about it again.