Epic's lawyers are most definitely not amateurs.
The filing also does not seem desperate or stupid at all. Granted, they are likely to have the same outcome as they did with the TRO.
However, the lawsuit will likely be very long and, regardless of the merits of Epic's claim (over which there was a long discussion in the TRO thread), they have an argument to make and even if the TI gets rejected, they likely do not want to put themselves in a position where, further down the line in the lawsuit, a judge or Apple's counsel might argue that "if Epic were so sure of the soundness of their argument/if they did not see the flaw in their argument, then they could have filed for a TI, and the fact that they did not shows how Epic themselves see how little merit there is to this claim".
EDIT: On the PR circus, I find the spin funny that Epic are "building an army" to fight Apple and the ridiculous Apple ad video and so forth, when in fact they are preventing almost 200 million people from enjoying their game, including the content many of these people purchased, for the sake of extracting more money.
Also, there is no way projections were not made for the different scenarios of implementing this strategy. There are certainly several excel spreadsheets with how much this can cost them, how long they can afford to go on without iOS and what the legal and marketing fees will be. No one is going "oh shi- we never anticipated this" at Epic.