I think you are overestimating how much Earth there was to scorch.
Unlike Brady, Kraft had no union to argue on his behalf and no CBA that he could claim was violated. There was no labor case so there would not be a big draw for the dispute to be heard by any court. He had also signed papers (of questionable binding power, granted, since guys like Al Davis DID in fact sue the league) that gave a promise that he would not sue the league that he was a part of.
His appeal route was solely to Roger Goodell himself, to argue that proper procedures were not followed, and we know how that would have come out. Goodell and 31 owners were solidly against him. He knew a waste of time and money when he saw it and moved on, apparently with a wink and a nod that doing so might help Tom Brady, which was bogus.
He faced reality of an unfairness that was also uncorrectable by his available legal avenues. You can say he was a rube for buying that caving in would help Brady, but that is the most serious reason to find fault with him, IMO.