Your core argument that football builds stronger camaraderie [than other sports or team-like activities] is unsupportable. There is no reason to believe that football is the key ingredient to lasting feelings of camaraderie. What if we just put high school students through a marines-style boot camp?
Also, everyone from the marching band still remembers marching through Disney World in 100+ degree heat in full marching uniforms. It was tough and it was a memorable bond we all shared.
Physicality is just one aspect of teamwork and camaraderie. Ever played in a (good) band? The levels of shared precision and intimacy required to synchronize on complex pieces of music for hours is difficult to put into words and certainly not to be taken lightly as far as camaraderie goes, you have to rely on the competence of your bandmates on a level that is relatively uncommon compared to most sports.
Also, everyone from the marching band still remembers marching through Disney World in 100+ degree heat in full marching uniforms. It was tough and it was a memorable bond we all shared.