Why would I run a rail-to-rail input opamp with its inputs at the rail even if higher voltage supplies are available
The AD8628 is a 5 volt op-amp and has a maximum supply rail of 6 volts hence why it can't run from +/- 5 volts. They use it here because of its phenomenally low input offset voltage of typically 1 uV. It also has an input voltage range that includes both power rails. It sounds like a good choice to me.