Importance of teaching as a PhD student to go into academia
If this is the US or in a place with similar traditions, then nearly all academics teach. Some more than others and some only at advanced levels, but generally, we teach. 

If you are good enough to be hired primarily as a researcher at an R1 university in the US then the hiring decision won't hinge much on your background as a teacher, but for most other academic jobs it will be a consideration, perhaps an important one. 

So, it is a good thing to get some experience with it, though it is time consuming the first few times. Post doc positions don't necessarily provide any teaching experience, though some do. 

Observing your own teachers gives you only a bit of the knowledge you need to put a course together, deliver it, and keep a bunch of students happy. 

But all universities have a complex mission, and teaching the next generation of scholars is a big part of it.