Other than finding the minor or major of a chord or finding the fourth or fifth is there any other purpose for the Circle of Fifths? I understand the sharps and flats for each chord is there.
All kinds of neat things can be found on the circle.
You mentioned The major and minor chords, the circle can give you what all the chords in a key will be. For example key of C. The C, F & G chords are the major chords and then right under the C, F & G are the three minor chords, Am, Dm & Em and the Bm7b5 is where? Yep right where it always is. It's a circle move it where D is at 12:00 O'clock, where is the C#m7b5? Yep right where it always is.
Got a three measure void leading to the Gm7 chord. What leads to the G, insert the D chord, what leads to D, insert to A chord, what leads to the A chord? Insert a E chord. Now which D, A or E? Kinda up to you. Which one fits best, D or Dm, A or Am, your choice.
What key is at 3:00 O'clock? A, how many sharps does it have? Answer, 3. What key is at 4:00 O'clock? E and how many sharps does it have? Four.
The circle can help you remember these memory pegs.....
Memory peg for the scales that have sharps = See God Destroy All Earth By F#irey C#haos.
Memory peg for what sharps will be in each scale = Fat Cats Go Down Alleys Eating Birds.
Memory peg for the scales that have flats = Farmer Brown Eats Apple Dumplings Greasley Cooked.
Find where these memory pegs are on the circle.
That F#irey C#haos also answers the question why it gets crowded at the bottom of the circle. There are 7 flats and 7 sharps ..... so they have to loop beyond the 6 O'clock position.
You have a choice of using the key of B or Cb. Which would you use? Five shaps are easier than seven flats.
You have a choice of using the key of C# or DB. Five flats are easier than seven shaprs.
You have a choice of using the key of F# or Gb. Both have five sharps or flats, flip a coin. Well, I think you would find B used more than Cb. We very seldom play anthing in C#, and I would use the Gb over the F#.
I'm sure the list goes on. Perhaps others will add more.