^ you neglect a few key components.
1. you need to factor in the impedance load on the amp. A 4 ohm load uses less current than a 2 ohm load for unregulated amps. If you have a JL slash or Alpine PDX or similar, then impedance isn't a factor. Impedance load determines output power capability.
2. amplifier efficiency depends on the Class. Class A/B is typically 50-60% at best, depending on the impedance load. Class D can reach 85% efficiency, again depending on the amplifier topology and load. I always take the amp class into consideration.
3. always consider the quality of the amp. A Boss audio amp won't make rated power. A Rockford Fosgate will. The latter is much more expensive for the same printed "wattage".
Average signal music being 1/3rd is a gross approximation, while quite accurate, doesn't help when sizing an alternator. If you want to prevent voltage dips, meaning you need to consider peak levels, or at least 2/3rd levels.
You need to consider what output you need at idle. more output at idle means a higher max output, and a larger load on the engine. a 4cyl engine's performance and fuel mileage will suffer when a HO alt is added. a V6 or V8 will just suffer fuel mileage. Good alt manufacturers will offer an output curve for their alt, showing output at various RPM.
When upgrading the alt you are upgrading all of the wiring associated with the alt. the new wiring needs to be properly sized, fused, and routed. Take your time on this so you don't have a rolling fire hazard.
Some cars use load detection (i.e. Honda ELD) to turn off the alt to safe fuel mileage. If this is the case, an HO Alt alone won't do much for you. You need to bypass or control the load detection to force the alt on in high current usage.
Finally, a battery bank needs to be considered if you plan on competing in SPL or turning the car off and leaving the tunes play. Battery banks are expensive and require skill to implement safely. They can be deadly if not done correctly.