The 15 degrees angle of bank in a climbing turn goes back to the old days when for cross-country flights one always set course over the top of the aerodrome rather than just climbing on track.
In order to reach the set course height it was quicker to get there at 15 degrees angle of bank in terms of rate of climb than at (say) 45 degrees angle of bank where the rate of climb is significantly reduced. One problem of only using 15 degrees angle of bank in a climbing turn in to the circuit is that in high wing trainers like Cessna 172 the lowered wing blanks out the pilots view during the turn leading to possible traffic confliction.
Using 30 degrees angle of bank in the circuit makes stuff-all difference in rate of climb while the time in the blank spot is less.