It's interesting to note that the decline in maths and science enrolments in places like Australia isn't reflected in, say, Hungary or South Korea. This leads me to believe that at least part of the issue stems from the way Australian (and to an extent Western) culture perceives technical fields.
I notice that a lot of people in Australia don't seem to view maths and science as essential skills. Instead, their value is often seen as being contingent on who you are or what you're using the subjects for. So, for example, if you're an engineer or a software developer, maths and science are viewed as important skills to have. But if you don't have any interest in such fields then our society gives you a 'free pass'; i.e. if you're not involved in something that explicitly requires maths and science, then it's OK not to be familiar with them. This manifests itself in many students characterising themselves as 'maths students' or 'humanities students' from a very young age.
This is vastly different from other cultures, in which maths and science are seen as essential skills in their own right. Without over-generalising, many Asian and Eastern European societies value the technical fields not only for their practical applications, but also because they equip people with the ability to think critically and problem solve. So regardless of one's career aims or interests, maths and science are invariably seen as indispensable to being considered an 'educated' citizen in these societies.
By viewing the study of maths and science through a utilitarian lens, I think you can only ever appeal to the people who are rationally minded enough to already have an interest in these fields for their own sake. What needs to be done imo is the establishment of a societal norm under which it is simply unacceptable not to be adequately versed in maths and science, just like it is a blanket expectation for people to know how to read and write.