Being a PhD student myself, I have to disagree with the last point: changing the world (actually, it was one of things that lured me were I am). While doing PhD you can be pretty certain that you won't become rich, it is also unlikely that you will change the world.
And comparing with science long-dead science luminaries is unfair - it used to be possible to make a (scientific) breakthrough working alone. But, say, for 50 years or so it is no longer true (the transition was smooth). When a field is fresh you can make a great in your garage; latter - not so.
Also, academia is a strictly top-down organization with all its consequences for creativity (in particular, having a great idea and skills at 17 yo will allow you to startup, put not - to assemble a research group). So if there is a great impact to the world by a PhD student, I can bet a lot, that it is because it was the PhD student's side project.
And comparing with science long-dead science luminaries is unfair - it used to be possible to make a (scientific) breakthrough working alone. But, say, for 50 years or so it is no longer true (the transition was smooth). When a field is fresh you can make a great in your garage; latter - not so.
Also, academia is a strictly top-down organization with all its consequences for creativity (in particular, having a great idea and skills at 17 yo will allow you to startup, put not - to assemble a research group). So if there is a great impact to the world by a PhD student, I can bet a lot, that it is because it was the PhD student's side project.