Checksum checking would catch some small fraction of uploads, but as already mentioned, there are many, many workarounds that are both easy and well known.
To defeat all these well known workarounds, copyright owners would likely end up registering thousands of checksums per protected work, dealing with all the variations as they find them. Not long before that process gets automated, and all anticipated variations get registered at the time of publication. And then you have a situation where the index of forbidden checksums is growing by several million entries per day.
And that's assuming private individuals don't get into the act. In law, everything we write or photograph or record is a new copyrighted work. How long till someone creates a tool to register the checksums for every comment we type on a blog? If that happens, we're looking at billions of new entries per day. More, if the tool also applies the "minor variations" algorithm.
Apart from the sheer overhead of managing all that data, and comparing every new item to them, which frankly I can't even imagine, you also create a rapidly growing probability of false positives. After a few years of this regime, not only would it be a coin toss whether each new item was allowed, it would also take several minutes to do the screening. So then you have a situation where people don't know, often until much later, whether their posting was successful or not.