Only want to say that limiting the snapshot in the same volume group as it's orignal lv really makes the idea of "logical" volume degraded.
For example, I use two hard drives with a RAID card to form a RAID1 disk and manage all it's physical space with volume group VG_SYS, and create my system volume and install my OS within it.Then I use another two drives to form a RAID0 disk and build a VG_DATA volume group on it, planning to use it as storage for unimportant data and snapshot.
However, I can't create snapshot volume in VG_DATA due to the limitation of LVM. Of course I can extend my VG_SYS onto my RAID0 drive and dedicate those pvs from RAID0 drive to my snapshot volume. But that would make my intention vague which separating logical volumes into important system volume group (redundancy guaranteed by RAID1) and unimportant quickly updated data volume group (RAID0 to increase I/O efficiency). Snapshots are meant to be updated and recycled very quickly so they don't need any redundancy. If a snapshot happens to be broken you just need to rebuild another one -- it's unlikely both your original volume and snapshot are broken at the same time.