It's not always processing power. Some of the older phones had known issues, for example the iPhone 7 often had a faulty audio IC, and the iPhone 6/6+ had low RAM relative to its larger screen size and bigger graphic sizes.
Prior to the 8 and XR, iPhones had Bluetooth versions 4.0 or 4.2, which meant things were slower to connect, and also meant lower microphone data quality. Apple hasn't done any customer education around this. A lot of people with older MacBooks have poor microphone quality when using AirPods - but it's primarily their computer that is the bottleneck.
