The throttling has nothing to do with battery life, its to do with current. When the battery begins to degrade, it becomes incapable of supplying the same level of current as it can when its new, meaning the processor won't get enough juice to function while under load, and thus the whole system shuts down to prevent irreversible damage to the components.
Anyone who's ever overclocked their own PC will understand the concept. Unfortunately, most regular people won't have experienced this, and whilst I can understand their frustration when all they see is "my phone is slower", most aren't understanding the simple science behind it.
You can have a phone that runs slower, but still runs, or a phone that powers off every time you open a heavy app because the CPU isn't getting enough power to function. Cant have it both ways.