It's not like the battery is actually empty. The phone is still able to run at 40% if it limits CPU power draw. As long as the throttling curve is accurate to the battery quality, it's all upside. A slow device is better than a turned off device. And if you want to keep your phone above 40% charge so it runs faster, go for it.

The root problem was not the throttling, it was the phone's inability to run at expected speed after a couple years.

The root problem is that Apple won't let you replace your battery.