1. The football team that has the knowledge and judgment you described are all A-players. A-players tend to not need a lot of process. One of the reasons we have project management and software methodologies and all that process is to help the team's B- and C- players perform predictably and consistently, if not close to as good as the A-players. If you actually found that mythical group of software people where each and every one of them knew the business in as much depth as your football players do, then yes, they probably wouldn't need as much structure. My experience has been these teams are extremely rare.
2. A football game is physically observable at all times by all stakeholders. Status needs no reporting. The score is known to all. The position of the ball is known to all. This is not true for software projects. Part of project management is providing visibility to stakeholders and leadership so that risk can be managed and informed strategic decisions can be made. This is why "Agile" emphasizes delivering working software as milestones. Different project management schemes use different methods to track and report status, but the end goal is the same.
3. A football game is already time boxed due to the structure of the game. There is a start time and a duration, it's separated into quarters, team activities are structured into downs, which aids the team in making tactical and strategic decisions. How would all these smart players "know precisely what to do" if they didn't know what quarter it was or how much time was left on the clock? Software does not naturally have any of this structure, so various methodologies seek to frame project with structure to aid decision making.
4. You really don't think any football team's leadership ever yells "We gotta get at least 10 more by halftime go make it happen!" You have to have intermediate milestones. Every sport I've ever played has had a coach or lead player barking the current goals at me. Guess what: That's part of the machine's oil.