I think the opamp doesn't need to work to V+, its inputs normally see over 2.5V less than the output is.
OTOH, it needs to be functional down to V- if you want the circuit to work accurately with low resistance loads. And even if you don't, it must have no phase reversal or it could blow up on such loads.
The value of R2 makes the reference run at a fairly high current when load voltage is high, and starves it when load voltage falls below 0.5V. An active sink would fare much better.