Thank you for the PM, FL.
Obviously I am not an airline pilot but I guess the attitude to this must depend on the exact situation, and also on the likelihood of "map shift".
Let's say you have navigated to a standard-ish 4.5D FAF, and you are pretty confident that's where you are. Navaids all checked, including the NDB/ADF. And you are established on the final approach track at the FAF.
There isn't much that can go wrong after that, just by flying the right heading. The distance to run is only 4.5nm minus whatever the distance at which you are supposed to be visual - typically around 2D so you have only 2+nm left to run. Obviously you will have a pretty good idea of the wind by then too. The ICAO procedure design criteria are pretty generous on NDB approaches. It seems over the top to require a constant monitoring of the ADF, during this very short distance and time.
Also, if "map shift" was that common, the whole concept of BRNAV and PRNAV would go out of the window. Planes would be wondering all over the sky. Your INS should be pretty stable for these short periods.
You can get a map shift with a pure GPS system if you are descending between mountains. But not in open terrain. Maybe Kathmandu but that is a VOR approach which should be accurate enough.
The proof of the pudding is in America, where millions of pure-GPS approaches have been flown, by a wide variety of operators ranging from private pilots to jet transports, and they have not identified systematic problems.