Wouldn't the Pats have the same opportunity to do the same to Goodell and his henchmen and expose all the dirt since he took office. I don't think that would be pleasant for him and his supporters either.
This was my first thought too. The OP makes good points but doesn't mention that discovery is a two way street. IMHO the league would be more concerned with discovery than the Patriots. I think the big difference between the league and the Patriots, regarding discovery, is the league is fused at the hip to the 'thorough', 'fully independent' Wells Report as well as all their subsequent public statements made from an unwavering moral highground. They never prejudged, they hired a thoroughly independent investigator, they had little contact with the investigator, and they accept the finding without any question whatsoever. Interesting thing about speaking with this kind of certainty from this kind of moral highground with an underpinning of your belief based on 'more probable than not something was generally going on', you absolutely feel deep down you are on shaky ground. And I'd bet money the league has plenty of communications that were born from that shaky feeling and contradict some of their statements and assertions. The Patriots, on the other hand, are already guilty and believed the bad guys. They are already speaking from the perch of the disliked. Which begs the the question what would be found on the Patriots communications, other than a personal embarrassment possibility, that is going to make the Patriots significantly more disliked?
I would also mention complex gray area of law when discussing a lawsuit. I'm sure it is a very good argument that the Patriots are contractually limited in their 'appeal of the punishment' options. However, the nature of the business of the NFL is complex and crisscrosses a lot of different laws and regulations. Every layer of complexity leaves that many more legal side doors (I base this belief on why the NFL loses its fair share of legal procedures despite massive deep pockets and ability to buy the best legal minds). With a case like this that appears to be heading in a way that may even touch a new area or two, the complexity should be a lawyer's dream for finding side doors.
From a headed to litigation but still a non legal angle, the precedent being set must be concerning to the league. And if it gets to a court it will get more concerning. Sure, if they win all the arguments involved with the Patriots, it would be a satisfying win. Yet the flip side potential must be giving them pause: (A) Every day this goes on the precedent is being entrenched a little more for a team to defy the league and not accept its decisions. Once one team does it another team that feels like it was wronged won't just roll over might do it. That's the nature of trailblazing a new path -- others now see there is a path to take.
(B) Procedural wins in court, even if not an ultimate victory for the Patriots, must also be concerning to the league. Even having a court say there is standing to litigate but the Patriots eventually lose the case, giving the Patriots standing to litigate is a blow to the league.
(C) Right now the league has most of the media and the public on its side (as inexplicable as that is). But, IMHO, the league is very close to its apex of support. This is as much support as they will ever get/see. So as they dig in to fight this protracted war, they will be fighting to maintain their support not to gain ground. What a shaky thing to do given their stance's underpinning is far from solid ground.