To play the saxophone properly, you need to know how to play on all keys. Generally, there are twelve keys in music and this means that I can sing a song in twelve different keys. As a saxophonist in a band, it is very important that you know how to play all keys because the singers in the band will have their preferred singing keys based on their voice range.
So, if the convenient singing key of a lead vocalist is the key of A and you can only play on the key of F; it would be quiet embarrassing for you as you would not be able to accompany or play a cool solo for that song.
What if the song even starts on your favorite key and all of a sudden, there is a modulation in the middle of the song to the key of G; what would you do?
Would you stop playing?
Lazy/Beginner pianist might be a bit lucky here because almost electrical piano have a feature called the transpose feature; they can easily use this feature and play on whatsoever key that is required of them.
It’s quiet easy to play all keys on the guitar as long as you know the pattern of one key.
This is why most saxophone players have a better understanding of music than many other instrumentalist. A good way to learn to play all keys on the saxophone is to learn a song on one particular key and also play it on all other keys.
The secret of learning to play the saxophone effortlessly is continuous practice. Do not stop practicing. The harder tutorial, the better for you.
Also, try to practice more on the circle of fourths and fifths. It is very helpful in the mastery of all keys.