Don't dissuade her. My mum did this to me, citing similar concerns about job prospects. I was steered towards a traditional academic degree, which was still interesting but not my true passion.
I lost motivation, got depressed and spent most of my time at uni drinking and smoking weed with other people who also felt "meh" about their degrees.
Still somehow managed to get a first but in the end the degree (in a humanities subject) was of no more use to me in the job market than an art degree would have been.
I got a good-ish job eventually, but only because I did a taught MA afterwards that included a professional qualification and a work placement.
I've spent my adult life feeling like I haven't fulfilled my true potential and have been in jobs that never really felt like the right fit, leading to low self esteem, feeling out of place and depression.
After doing a lot of soul searching, pivoting and further retraining I'm now (aged 36) finally in a job I like, in design.
I carried on doing art on my own and at leisure evening classes and I'm now applying to do it part time at college, because my biggest regret in life is listening to my mum and not pursuing it when I was younger. I should be grateful that she supported me through uni and I am, but also deep down I feel resentful that she killed my dreams before I even got started.
I think parents like mine and the OP are well meaning but have a lot of misconceptions about creative careers (my mum worked in science).
Your DD may or may not go on to be a portrait artist. There are other options available and she can see for herself when she goes to uni and when she graduates what is and isn't a viable career path.
I know a number of people who studied art, they've done a range of things afterwards - one is a full time photographer at a newspaper, another ran art workshops for people with mental health issues and creative play classes for children, others work at art galleries. Some create art for exhibitions and also run classes and workshops, and do various freelance projects.
There are also jobs like graphic design, UX and UI design, interaction design, content design, videographer etc. They're available in both the private and public sector, some charities, start ups etc.
My current job is in one of these fields, at a large public sector organisation and I'm working towards senior level (can earn up to £60k), even more in some private sector companies.
You do need additional skills and work experience/portfolio but this can be done alongside the main degree. I did most of my learning from places like Udemy (free short courses) and got experience by doing free work for charities.
If you're worried about the cost of a degree she could also consider an HND at a college, which is much cheaper and more practical. They also have good links with local employers.