Well, football is a lot more tiring than, using your example, basketball is. Football games generally occur once a week per team or, at times, twice a week. If football seasons go by the postseason system, the season would have to be a lot longer and demand a lot more from the athletes. I doubt a full season with a postseason would even fit in a calendar year, so no rest would be given to the athletes. Also, football is outdoors and pitch regulation is very important. A 90-minute match would probably wear down the pitch a lot already, so if it has to accommodate for a few matches per week, the quality of the pitch would be really bad and they'd probably have to use synthetic grass.
To be honest, I'm not too sure if it's the American culture or just the sport. Even in Hong Kong, basketball tournaments are determined by a system similar to the NBA postseason. In my opinion, more matches would provide a sufficient amount of data to determine whether or not a team is worthy of winning the series rather than a 2-match system where the aggregate results determine everything.
