MOSFET LDO, how does it work
Your circuit works as an LDO regulator but only because there is a 5 volt power source that can lift the gate 5 volts higher than the input supply voltage. This means that if you only need 4 volts gate-source there will be virtually a zero voltage drop-out performance.

All linear LDO regulators that I know of don't have this useful but impractical voltage source hence they use PMOSFET transistors.