The logistics of a ballot would be a nightmare.
How would people ensure they and partners/family had tickets?
If to do this they said all registered at one address can be entered together then people would register 50 or more at one address. They could limit it to 4 or 6 per address but then what if an address, such as student digs, had more than that?
These are just 2 or may potential dilemmas a ballot would raise.
and I hate the idea of there being a ballot anyway for all the reasons others have given.