Hi! 
Could a lightweight version of paraview be built with a QML interface and compiled to webAssembly to run entirely in a browser? Has anyone attempted this, and what would be the main technical challenges?
A QML front-end is definitely possible - see this blog post for an example.
Compiling it all to WebAssembly is theoretically possible, but there are likely some incompatibilities in ParaView-specific rendering classes when going from OpenGL 3.2 to WebGL that would need to be addressed. WebGL has a reduced feature set compared to OpenGL. VTK is in much better shape in that regard, which is good news.