"Sellers could cut them out by raising their prices so that demand matches supply."
Ding! Ding! Ding! This is the correct answer. What most people don't understand is that the venues are charging less than people are willing to pay. Demand is greater than supply and so the price goes up. Scalpers are there to correct the situation. The only way to "beat the scalpers" is to price the tickets appropriately, meaning to "auction" off the tickets to the highest bidder. Then, if the performers/venue feel the prices are too high, they can perform another show. This is the way the free market economy works.
The hardest part of climbing the ladder of success is getting through the crowd at the bottom.