The problem is what you do outside the file: even if it contains a working decompressor, you have to actually run that decompressor, which most likely requires specifying the byte offset and doing some other work to extract it. And then the decompressor needs to shorten the file even past the length of that byte offset and extractor, which can't be done with reasonable probability.

There are some formats which search for a valid header anywhere in the file, but then they'd get tripped up by all the mostly-valid headers that don't actually yield a decompressed file.