Yes, I tend to use the MeshEdit objects as the assets since it allows for quick iteration times (I usually use the tool for level geometry).
You can still export to .obj files and import those assets in a new Mesh Edit object, or load them into their own Game Objects. Saving a Mesh Edit object as a prefab has some problems but I'm currently working on an "export as prefab" option that will be available in v0.4.
An option which I use a lot for duplicating objects is to copy/paste the faces into a new object:
1. Go into Mesh Edit mode, select all ("A") and copy the faces.
2. Create a new Mesh Edit object and go to Tile Edit mode, then select the tileset from the dropdown that the original object used (Textures won't be copied unless you do this step).
3. Switch to Mesh Edit more and paste the faces, creating a full copy of the original mesh.
This is definitely a workaround, so I'll try to work on more streamlined options for duplicating a mesh for future versions. Thanks for bringing the issue to my attention!