There are way more reasons for Brady to not give up his phone. You want to compare everything to law, then the NFL has no subpoena power. Why should he give up his personal phone?
That's exactly right. The NFL has no subpoena power, because this is not the United States judicial system. This is the NFL, an organization that has it's own rules,... and if you wish to be part of it, then you agree to abide by its rules and its authority, and the authority of the commissioner who is charged to act in the best interests of the game.
Probably the #1 thing that the commisioner is charged with that is not directly financial, is to protect the integrity of the sport and league. Whether deflating balls actually caused a game to be compromised isn't the issue...it is the
perception that a game could be, that is enough for a harsh penalty.
The only mitigating factor that I see, is that the NFL has let QB's take liberties with the game balls in the past....deflating/inflating them is only one step away from rubbing dirt on them to get a good feel. Hence, I think the penalty was too harsh, because the NFL has a degree of complicity here.