Firstly i dont know who said you cannot use the external drive on another computer...you can.
If for example you use Acronis and save to the External drive and have the original Acronis disc,this becomes your bootdisk.If you do not have the original Acronis disc,you need to make the boot disk.(create Bootable Rescue Media)
This is how i do it:
Use Acronis to make a system image.
Save the backup to the External Drive,named Acronis backup.
If you have a system problem,insert the disc and plug in the drive,Acronis will point you to the backup on the external drive,select this to restore your machine.
I currently have 3 systems backed up to one drive,though have not had to use them yet.