Anyone who has read my (numerous, long

) posts on this subject will know my opinion - if you didn't fall asleep whilst reading. But just in case...
I think the "something to fall back on" argument is flawed and I agree with studying/pursuing what you love. One thing many determined performers have is a really clear vision of what they would like to do - lots of people don't have this. It seems daft to me to deliberately choose something different.
What does seem sensible to me is to look at what you can do to earn money
while you are trying to make your living as a performer. I think this difficulty is the main reason people have to give up performing - because there's not enough money in performing itself. If your dc can imagine earning their living doing something else and acting as an amateur, then that's a really good idea - and to be recommended by all right-thinking people who want their offspring to be able to get a mortgage one day

- but if you want to try to earn a living as a performer then you need to know about the business (or do some work to find out about it) and be prepared for the most likely outcome: very little money, infrequent performing opportunities and the need for a flexible job to pay the bills.
You are very unlikely to earn money while you are trying to make your living as a performer using your
degree-level skills: that, to me, is the flaw in the "something to fall back on" argument. Most jobs that need a degree also need commitment - and that's the one thing a performer can't guarantee.
I think the time to choose a "sensible" degree is after you have given the dream your best shot - otherwise there is likely to be the nagging "if only I'd had a go" later in life.
I would recommend that any young person wanting to go into the profession tries to find some struggling actors to talk to - and asks them to be really honest about their careers. It can come as a shock to realise that despite excellent training (and considerable talent)
most actors are unemployed (as actors)
most of the time.