Well, first: does reading a global variable at some point create a copy or not?
Having to do the checking on each write has the slight disadvantage of slowing down writes. For that matter, we still have to consider how heaps are organized.
For example, in my current stop-and-copy, always-copy-on-message-send, each heap has several semispaces. Semispaces conceptually belong to only one heap. One of the semispaces is the current semispace, the one that is being allocated into. The others were semispaces that were received during message sending.
When a message is sent, it is copied into its own semispace, then the semispace is added to the list of "other semispaces" held by the heap.
During a GC, the GC copies all semispaces into a single new semispace, then the heap releases all the other semispaces and sets the new semispace as the current semispace.
In theory it should be possible to reduce slightly the GC overhead by just copying some (but not all) semispaces into the newest semispace: this is basically an incremental GC
Edit: As an aside, the advantage of leaving it "undefined" is so that we can change the implementation of global variables without committing ourselves to stone. "What, you kept a table in a global variable and expected to use that to communicate with other processes? Well, sorry, but that won't necessarily work (or not work)"