I was digging through the court records on the Carol Publishing case I referenced earlier, and there Paramount apparently did not actually collect any monetary damages. The parties reached a settlement where the publisher simply had to destroy all remaining copies of the infringing books they had in stock. Similarly, I would expect the studios here would require Peters and Axanar Productions to destroy (or turn over to them) any sets, props, costumes, and models developed in connection with Axanar. CBS and Paramount would likely be satisfied with that and not seek further monetary damages.
Peters & Co have entered into commercial deals with third parties. This case is different from the one you quote for that reason - and just because a party doesn't follow up something to which they are entitled to in one case doesn't mean they won't in another.
Often it will come down to whether or not it is in their overall interest to pursue a financial judgment. In the case of the example you referred to, the earnings from the book were probably so low as to not make it worth pursuing the judgment. In this case I think it will depend on benefit vs cost. There is also the question of monies owed to other parties, such as the donors, if the copyright has been breached. Since we're talking about over $1m it could well be that there is a class action against Peters & Co on behalf of the donors, along with any other claims arising out of the termination of the production, and that could also impact what the studio does in terms of enforcement.
But I do generally agree, I suspect the primary motivation of the studio on this occasion is be to send out a message to the fan community illustrating what they will and won't tolerate.