I don't think WebGL will have any affect here. The requirements for runtime asset format vs. interchange formats are completely different.

Generally runtime formats are designed to optimize out all the cruft that interchange formats like COLLADA and FBX have to keep around in order to be portable.

This is the reason most engines (including ours, PlayCanvas) use custom model formats at runtime. They are specifically designed to work well in a particular engine.

In Autodesk's defence the FBX SDK loads COLLADA and OBJ files very well, so we're able to support all these formats easily. The downside is that other software (such as Blender) has poor FBX support because they can't (or don't want to) use Autodesk's SDK.