I think it’s tricky because while it doesn’t seem very common nowadays for children to pay back their parents for college education (formally, at least), parents want a good ROI on their child’s degree-- meaning, they want their child to be self-sufficient after college and don’t want to continue funding their child. If a child were to ask to have a parent fully fund a degree in a tricky or very low-paying field, I would hesitate. Nothing to do with “prestige”; I’d be just as likely to hem and haw over a music degree (low paying, few jobs) over a law degree (virtually zero jobs).
I think having multiple children can also complicate things; if my firstborn wanted to enter a fast-growing high paying STEM and they were good in that field of study, I can’t imagine having doubts. But then, if you have a second who wants to major in English or art history or whatever… and then you hesitate, but it’s “why does she get to major in what she wants but not me???” or whatever.
With ChemE I can’t imagine I’d hesitate. On principle, I’d like to fund whatever my child wanted to study-- but I wouldn’t take out massive loans for them regardless of field. If they wanted to study in a traditionally less lucrative or more competitive career, I’d make a bigger effort to ensure a.) they know what they’re getting into (as one mentioned above, a daughter who thought forensic chemistry was more like CSI than lab work) and b.) they have a tangible plan for internships, fellowships, etc. to gain better chances at employment, have back-up plans in case they can’t find work, have evaluated necessities of grad school, and understand (and accept) what it means to make 40k a year vs maybe growing up on a household of 100k+.