To be clear, I'm not suggesting TopoJSON as an alternative to GeoJSON. I like GeoJSON and was loosely involved with the working group that created and updated its spec.

I'm just saying that for the specific task I mentioned GeoJSON or any format such as shapefiles that store polygons individually naturally leads to the "sliver" problem.

A nice processing pipeline is:

1. Convert GeoJSON to TopoJSON.

2. Run the simplification on the TopoJSON.

3. Convert the resulting TopoJSON back to GeoJSON.

The TopoJSON GitHub has tools for each of these steps.