and I don't remember it ever causing anybody a problem.
Well that just shows that you don't remember very well. The reason CDFA approaches were developed (originally using stopwatches and/or DMEs before the advent of fancy FMSs) was because of the high number of accidents involving messed up NPAs.
Apart from questions of stable approaches in principle, flying along at MDA meant that getting visual too soon and descending below the ideal approach angle to stay visual or just because you have seen the runway is almost as risky as getting visual before the MAPt but well after the ideal approach path and ending up high and fast.