They didnt appeal the team issue because taking the NFL to court would be a losing hand.
Based on the way the NFL is structured they had to take the NFL to court outside the internal mechanism. Because there is no internal mechanism to challenge NFL decisions.
That was the NFL equivalent of the nuclear option.
And if this issue was going to court and you are starting to be able to search things that the Wells reports couldn't get to like Brady's phone Kraft would have gotten killed.
Just by doing it would have sent shockwaves and would have likely destroyed Kraft's standing in the NFL ownership Cabal.
This was all probably scripted from the get go and Kraft had to shake his fists enough to appease his fans then back down without actually doing anything.
I suspect that Kraft, who likely has Goodell on speed dial, is going to try to leverage this to reducing Brady's suspension.
If there is no reduction then it tells you have weak the Pats argument is.
Probably goes down to two games. Still sends the Pats to Ralph Wilson without Brady which will be big.