New answers tagged topology
Have you tried using MapShaper? I've found this to be a good way of generalizing polygons; there's also an offline version if you want to download the code. An alternative could be convert this to GeoJson, and then TopoJson which supports "topology-preserving shape simplification" https://github.com/mbostock/topojson
GRASS is topology-aware. You can use v.generalize from the Processing toolbox to simplify polygons and if the input data is topologically correct so will the output.
You will not be able to delete a feature class which participates in a topology. You should first exclude this one from the topology. You can either use a GP tool Remove Feature Class From Topology (Data Management) or do it manually via Removing a feature class. If you don't really need to recreate/replace a geodatabase object (such as a feature class), ...
I think you will have to use something like v.build.polyline. Edit: From the man page: v.build.polyline picks a line and from its start node, walks back as long as exactly one other line of the same type is connected to this node. ...[polylines] sometimes [are] broken into their constituent straight line segments during conversion from one data ...
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