Is it typical for STEM students to be responsible for coming up with their own thesis projects?
I would say it is not typical to expect a student to come up with their project completely on their own, although I will admit that I have done this with one particular PhD student who had already demonstrated in his master's project that he was sufficiently capable that it made sense to let him "drive" the project so long as it was something I felt comfortable advising. This was also possible because he had a secure source of funding that allowed us to do this.

However, for a typical student, such a route would be very risky and quite prone to failure, especially if she is just beginning her graduate work. I would not expect the student to be able to come up with independent ideas for a project until well into the course of the PhD program.