Bear with me here, I’m still new to these forums.
Warning: Spoilers (but seriously just finish the campaign already people come on )
I agree that the shard seems to have been blown off the Traveler, not cast off. In the intro for D1, the Speaker says the Traveler was crippled when it drove back the Darkness. This seems to say the shard was broken off forcibly. If you look at the Traveler before it reawakened to defeat Gaul, it has peices of its shell missing along the bottom. This seems to imply that the Traveler broke up along the bottom, leaving behind peices of its outer shell along with some shards of what it has inside it.
Also has anyone else noticed that the Traveler has and inside similar to a machine, but built in layers? I noticed in the intro cinematic that the Traveler is “drawn” in a set of layers, starting with simple lines, but gaining a blueprint-like feel before the final alabaster shell covers it up. It seems to me that the real source of the Traveler’s power comes from something it is containing, and the actual sphere is simply a kind of suit it has to help conduct its energies, especially since we know the Traveler is a “great machine” by reading the bits of lore we have on the Eliksni.
On another note, where is the City/Tower located? I know the Shard (the EDZ one is the one I’m referring to as the capital-S Shard) is in the European Dead Zone, somewhere in Europe. The large portion of the Traveler’s shell is in the same area, along with many other shards.