I am wondering what the purpose of the "mouthpiece exercises" is. Also, why is it importasnt to get a certain pitch?

I do understand the pitch is somewhat standared based on the pitch of the instrument it is designed for, but I dont see the value(?) of mouthpiece exercises??

Someone enlighten me and my ignorance.

I did a bit of resarch, I still dont get the value of practicing without the saxophone.

This is definitely worth doing. Producing the proper pitch and a good "whole" sound on the mouthpiece alone is a great training exercise for showing you where your oral cavity should start (before voicing), and it also can prevent bad habits, i.e., if you are biting too hard, you might not realize it through the horn, but you'll never get the right pitch on the mouthpiece alone. I had a teacher in college that really harped on this, and I found it (along with long tones) to be one of the best things you can do to improve tone quality and control.

What mouthpiece/facing/reed strength are you using?

(a quick write up about its importance : https://www.bestsaxophonewebsiteever.com/what-playing-on-the-mouthpiece-alone-can-tell-you-about-your-pitch/)