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>Apart of few exceptions, professors need PhD students more than PhD students need professors.

Can you elaborate on this? I'm not disagreeing, but colleges/professors certainly like to project the opposite in many cases

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Professors depend on grant money and they need to push out papers to be competitive in grant applications. The vast, vast majority of work in research is done by grad students. Without students, professors would have to do everything themselves or compete with industry for talent they can't afford.

Students by contrast need professors for training and advice. Whether they receive these from their advisor depends on the lab. In bigger labs junior students learn more from senior students and post-docs than professors.

Just as an anecdote. I was in a doctoral program in engineering, and I mastered out into a 90k/yr job (this was in the early 2000s) writing cplex code to optimize supply chains. A buddy in the PhD program was doing nearly identical work for a 15k/yr stipend.

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