MLS would be doing fine by now, if US hadn't prematurely switched allegiance to GPS. We are still awaiting CatIII LAAS thirty years later, but hopefully it will appear before long.
MLS avoids the traffic throughput limitation(higher frequency means less multipath), but it is no good unless everybody is fitted.
These days FMS can generate any curved approach path, provided it is within the MLS "cone"---no need to have "a series of waypoints with straight sectors in between"
Just to set the record straight:
1.The ICAO-chosen MLS version(TSRB time-referenced scanning beam)is an Australian invention.
2.The loser (doppler) is an entirely British show. There was little difference between the performance of either system, except that doppler was easier to check for integrity with ground signal monitor. You can do it from a single monitor, whereas TRSB needs checking across the whole cone.
Keith