I'm convinced there must be a way of using ASTs to do more intelligent diffing of a given programming language, but I'm far too lazy to find out for myself.
It's not necessarily about the load, it's about the algorithmic complexity. Going from lists (lines in a file, characters in a line) to trees introduces a potentially exponential increase in complexity due to the number of ways the same list of elements can be organized into a tree.
Also, you're underestimating the amount of processing. It's not about pure CPU computations but RAM access or even I/O. Even existing non-semantic diff implementations are unexpectedly inadequate in terms of performance. You clearly haven't tried diffing multi-GB log files.
Log files wouldn't fall under the banner of compiled languages or ASTs, so I'm not sure how that example applies.
And I'm aware that it can lead to O(n²) complexity but, as others have provided, there are already tools that do this, so it is within the capabilities of modern processors
Yes there will be cases where the size of the search space will make it prohibitive to run in reasonable times but this is - by merit of the existing tools and the fact that they seem to work quite well - an edge case.