This isn't about making the battery last longer. It's about making the phone work at all. It has to do with battery chemistry.
Old batteries don't just "last less". They also have an increased internal series resistance. That resistance actually limits the amount of power you can pull out of it. The more current you draw, the more energy is wasted as heat, and the lower the output voltage. As internal series resistance increases, it becomes physically impossible to get more than a certain amount of power out of the battery, and this limit also decreases as the battery drains during a given discharge cycle. It's a hard physical limit. The I-V curve just never hits your power target. If you try, your voltage sags and then the phone shuts down. This is what triggers a common syndrome in old devices, where the battery meter shows 30% but then you try to open up a CPU-intensive app and the device immediately shuts down. Chances are that's not the battery meter being wrong or miscalibrated: there really was 30% charge remaining in the battery. It just wasn't capable of handling that much power draw at that charge level. There's 30% charge remaining and there's a hidden limit as to how fast you can drain it.
It's almost certain that what Apple did here was start throttling phone performance when battery voltage sags below a critical threshold, to prevent hard shutdowns. On older batteries, this would appear as a performance limit as the battery empties. But it was never about making the phone last longer. It's just a physical limitation. The alternative is your phone shuts down. That's obviously not good.
The right solution, of course, is to have a notification or something that tells users when this is happening. Something along the lines of "Your battery cannot supply enough power to keep your device working at full performance. To maintain optimum performance, a battery replacement is recommended.".