> The duplicated edges tend to fall out of sync when edited so that abutting areas end up overlapping or not quite meeting.

I assume by 'get out of sync' you mean that the two closed way areas that used to perfectly share an edge are no longer identical along that edge and there are either holes or overlaps where one of the ways has some extra nodes/is missing some nodes somewhere in between?

I'm not quite sure I follow that argument. Deleting or moving a node always affect all parent ways and cannot make them go out of sync. When adding a new node into a way, pretty much all editors simultaneously add them to all overlapping ways that share the same way segment so that they are still in sync and attached (and if they don't, they shouldn't be anywhere near users who don't know exactly what they are doing). Detaching the ways from each other is actually harder than keeping them overlapping and really has to be done intentionally.
The one way that overlapping or not quite seamless areas can happen is if they are created that way and were never attached in the first place. Often there is a reason why there's a gap in between and if there isn't, they can simply be attached by merging the nodes to make them overlap.