To clarify, in the US you are allowed to view your medical records. If you want copies, providers may charge you and they are allowed to do that. Process notes/therapy notes don't necessarily fall under that category depending on how a T stores their documentation. Additionally, mental health providers are allowed to refuse to let their clients see their notes if they believe that it would be harmful.

In the spirit of therapy, you can ask anything of your T, but in general they won't alter their documentation. You can have an addendum added however, although in certain circumstances they can refuse.

I personally don't see a need to request and keep (or read) my therapist's notes, but I can understand how others might. But, it's important to know that it probably won't be as easy as asking and then a day later getting copies.