Also, does anybody now fly an NDB or even a VOR without an FMC overlay using LNAV or the equivalent?
In real life they probably don't. But when testing a candidate for an instrument rating in the simulator and if he requires to renew his endorsement on the ADF or VOR, then he must demonstrate competency on each of those navigation aids. Using an over-lay and VNAV/LNAV is not a valid test of his flying skill at conducting those non-precision approaches.
Frequently it is noticed that the candidate has significant difficulty in tracking in crosswinds when flying these approaches as sole navaids especially raw data. Which is precisely the purpose of checking them on the basic navaid rather than allowing the autopilot/FD to fly the overlay which is by no means proof of the pilot's flying ability.