but each of those servers that hold the file the hash points to could have DMCA takedown notices filed against them...
The NFT owner, or any other interested party, could just keep a copy of the file offline. An IPFS content ID (hash) is normally used to retrieve the content from the network, but it can also be used simply to verify that you have the correct data. Also, anyone with a valid copy of the file can add it back to IPFS at any point with the same CID, making it available once again to the rest of the network.
There is also the fact that this is a trademark dispute, whereas the DMCA is for copyright claims. Presumably the NFT creator took the pictures in question and holds the copyrights to them. If so, those hosting the files on IPFS would be doing so with the permission of the copyright holder; moreover, they are not directly involved in the trademark dispute as they are not the ones allegedly misusing the brand. I'm not sure what legal theory could justify going after anyone hosting the files.
The whole point of NFTs is them being unique, right, so if you are spreading an NFT image across a lot of servers aren't you defeating the point?
It's the NFT which is unique, not the image. Generally speaking the image itself is available to everyone, not just the NFT owner. This is something like the difference between cheap unsigned / unnumbered digital prints of a famous artwork and a signed & numbered original, except in this case the signature is the only difference—the images themselves are exactly the same.