I read through the arguments, and while I think these publishers need to be cut down to size, I actually think the three specific arguments they are making in this lawsuit are not very strong.
The first pillar of the argument is that peer review is unpaid labor (true) AND that scholars have to peer review with these specific publishers in order to be published by those publishers. That's a bold claim and I don't know that it is substantiated, or provable. It's very hard to prove that kind of causality, and while it is widely accepted as true that you have to peer review, I don't think it's easy to prove that you must review for a specific publisher to get published by that publisher. And it also may be true that your institution requires you to peer review in order to get promotions and pay raises, but that's unrelated to this lawsuit and is a problem with universities and not publishers.
The second pillar of the argument is that the publishers agree not to compete with each other by requiring submitted manuscripts to only be under review in one journal at a time. This argument does not make sense to me because you can choose your publisher, and I think the inverse of this is actually worse for everyone. There is a lot of labor involved in managing peer review, and imagine if that labor was being done in multiple journals simultaneously. That's a lot of wasted time and resources, and it's wasting more peer reviewers and editor's time. From a business's perspective, it does make sense to say "if you work with us you can't work with others at the same time," and I don't agree that this is antitrust behavior to do so. I think this is a normal and reasonable business practice. Imagine if you were a bakery and someone ordered a cake but by the time you finish baking it they say "actually I got a cake from someone else, I won't pay for that" -- you've still done the labor but your customer jilted you and won't pay for the labor. You still have choice of bakery, it's just that once the cake is in the oven you do have to buy that cake. That's more like the practice publishers are doing here, rather than reducing competition. As an aside, removing this rule may cause copyright havoc -- if a scholar forgets to inform one of many journals they submitted to that their work has been published by another journal, and the second journal also publishes the same work, then those publishers have a copyright issue between them. Lastly, I think this actually makes the risks around publishing poor quality work even worse. If publishers are incentivized to act quickly for fear of being jilted, that may incentivize even worse vetting practices.
The third pillar of the argument is that the publishers require you not to talk about your work while it is under review. This is demonstrably untrue, as most major publishers allow preprints prior to publication. I don't know what they are getting at here or why. I think they want to make an argument about who holds copyright but they don't outright say that.
Even within their statement, they make a different, much stronger argument: "Deutsche Bank aptly describes the Scheme as a
'bizarre' 'triple pay system' whereby 'the state funds most of the research, pays the salaries of most of those checking the quality of the research, and then buys most of the published product.'" In my opinion, this is the real antitrust behavior, and the fact that this is not among the pillars of their argument likely means there aren't clear laws around this.
My spouse suggested, and I agree, that they might be trying to trigger an FTC inquiry because the FTC can go more deeply and look at things beyond the specific letter of the law. If so, I hope so. If not, I don't think this lawsuit is very strong.
Things that publishing companies should come under fire for:
consolidation of publishing companies thereby reducing competition, publishing companies absorbing society publishers
publishers having copyright rather than authors retaining copyright
subscription models in general charging exorbitant prices to libraries for research that was publicly funded and should be openly available
unpaid labor of reviewers and editors in general whether or not that has bearing on the ability of those reviewers and editors to publish with those publishers
lack of thoroughness of peer review (publishers cut corners constantly and put onus on reviewers that should be on publishers)
diversity of the editors and authors / who is being published
Many of these behaviors do not really fit under antitrust laws, but perhaps consolidation and copyright. I think the biggest problem is subscription models, so I do wonder why this is not the thrust of the argument.