No, that's not the only solution. The other solution is to make the tickets non-transferable. Require those at the gate to present their ticket along with a piece of photo ID matching the name on the ticket. Problem solved.
The point is to get the tickets to the people who want them the most. I think a lottery does a poor job of that.
Seats at performances are scarce resources. We have an efficient and fair mechanism for allocating scarce resources: the market. Raise ticket prices to the market-clear price and be done with it.
Charging market rates for the tickets means some popular events will go for thousands of dollars. Artists don't want their fan demographics to get skewed by that.