Also you need to do climbing and descending turns whilst in the circuit, and the only safety aspect is that you don't exceed 15 degrees of bank angle whilst climbing. I think the reason is that you are near your stall speed in the climb, and if you bank too much, you load the plane with too much G which brings up your stall speed (as the square root of the G.) Also at slow speeds 15deg of bank will give you a small enough radius of turn anyway.
At 30 degrees of bank the stalling speed increases by only 7%. I think the main reason for limiting bank angle to 15 degrees in a climbing turn in SEPs is that increasing bank angle above 15 degrees means the rate of climb is considerably reduced, assuming one is lowering the nose to maintain climb speed.
One important aspect to mention is spiral stability. In a climbing turn the aircraft has a tendency to over bank so one ends up "holding off the bank" with aileron opposite to the turn. (Think of the different spiral staircases the wingtips are following and the difference in airspeed and therefore lift). This can vary a little between types but in a descending turn one generally has to "hold on the bank".
The importance of a well flown climbing turn,especially for inexperienced pilots, is that the first one after take off is executed relatively closely to the ground - 500 feet ago minimum? It's near the ground that you are more vulnerable. A bit of over bank and airspeed below the best climb speed and throw in an engine failure and you have all the ingredients for stall/spin unless prompt action is taken.