Simple 15W Amplifier

That's 11 V peak. A simple, typical power amp circuit will require significantly more than just 1 V of headroom. I haven't looked into this but I assume some of the Rail-To-Rail techniques used in opamps could be used in a power amp too.
Don’t overthink. I believe he/she is working on the school assignment. A traditional 3-stage amplifier with single pair push pull emitter follower will do.
 
A diff amp ( Long tailed pair ) one VAS transistor feeding a pair of output NPN's / PNP's will do for 15W. duno about +-12v tho.
You can add constant current to it and a current mirror to make it nicer , and maybe a darlington output pair.
Can't the supply voltage be higher?.
 
@Els_Chaos Simple design. Can get even " simpler " if you remove the constant current and current mirror , maybe darlington output pair.
 

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Looks good. 100uf on input is to much, also you can add a low pass filter for EMI , AM reception .
Why a pot in the feedback loop?
If you have trouble with thermal runaway , tho you shouldn't. Q9 glued to Q10 or on the heatsink.
C5 might need to be bigger ( 47 - 100p ).
Small 47 ohm resistors in the ltp emitter resistors might help.
Should work fine in real world as it is tho.