The Constitution for the United States of America is the supreme written law of the United States. It lays out a set of powers for an elected legislature called the Congress, reserving power over everything else to the several states (50 at last count). The Congress regulates commerce across state lines, but each state regulates commerce within its borders. This would seem to allow each state to set its own drinking age.
However, the Constitution has more to say: "The Congress shall have power
Each state has power to set its own minimum age to purchase and consume "drinks" (beverages containing ethanol), but the Congress will not grant highway funds to states whose drinking age is less than 21 years. To make it easier to enforce this law, states have established separate licensing for establishments that serve food: "restaurants" admit minors, and "bars" don't. States also limit the amount of drinks that restaurants can serve.
A "rock band" is a group of people who routinely perform live rock music together in front of an audience. A rock band can choose to perform in any of several venues: a recording studio, a stadium, a theatre, a restaurant, or a bar. Problem is that many people won't spend money on a record they've never heard, and radio stations charge an exorbitant "independent promotion" fee to get a record played. Stadiums and theatres also charge an exorbitant venue fee, which many local rock bands cannot afford. This leaves restaurants and bars, and very few restaurants find it profitable to let rock bands perform on their premises.
Local rock bands also have trouble getting their records heard on the radio.
Therefore, minors have nowhere to turn to see a local rock band perform. A captive audience of teenage listeners is exactly what the largest publishers of recorded music (hereinafter "major labels") want, as they find it easier to cultivate a Britney Spears or *NSYNC than to find real musical talent. Instead of buying records at shows, they buy what they've heard on the radio, which the major labels control, or what they've seen in stadiums and theaters, which the major labels also control.
Google has more information on how the legal drinking age has affected the local music scene.