An interval exists so players can rest. In American sport it became a production with its own audience, and the reasons are institutional rather than musical.
Marching bands filled the gap first
College football grew alongside military-style bands that already existed on campuses, and the interval gave them a natural place to perform in front of a captive crowd.
Field formations and drill routines developed specifically for the space and the viewing angle, which is why the performance is designed to be read from above.
The band became part of the institution's identity, and for many schools the halftime performance carries as much tradition as anything the team does.
Ceremony attached itself to the same slot
Recognitions, presentations, homecoming rituals and alumni events all need a moment when the crowd is present and nothing else is happening.
Concentrating them in the interval keeps the game itself uninterrupted, which is a practical arrangement everyone benefits from.
Over time those ceremonies accumulated, and the interval lengthened to accommodate them well beyond what player recovery required.
Broadcast made the interval valuable
A scheduled break with a known start time and duration is inventory that can be sold, and it is the only substantial gap in a sport otherwise structured around continuous play.
Television needed the audience to stay, which meant the break had to be worth watching rather than merely tolerated.
That is the point at which the interval stopped being a pause and became programming with its own production budget.
The performance grew beyond the venue
Large-scale halftime shows are staged for a viewing audience rather than for the stadium, with camera positions and timing determining the design.
Spectators in the stands often see a worse version of a show built for people at home, which is a familiar trade-off in modern sport.
Setup and removal must fit inside a fixed window, so the engineering of getting equipment on and off the field constrains everything about the performance.
Other sports adopted the format unevenly
Sports with natural breaks have imported the idea readily, while those with continuous play have struggled to insert one without disrupting the contest.
Cricket and other sports with existing intervals were well placed to adopt it, which is why strategic timeouts filled with entertainment appeared quickly in the franchise leagues.
What began as a chance for a band to march has become a template that sports worldwide now use to monetize a pause.

