When theoreticians talk about LZ, they mean unlimited LZ, not LZ within a limited window. If you are only interested in data compression, the existing algorithms with limited window size should be much faster, use less memory, and achieve similar compression, except in some rare cases.
The primary motivation for unlimited LZ is text indexing. You can build text indexes based on LZ parsing and achieve ridiculous compression ratios with repetitive data (e.g. versioned documents). The query performance depends on the length of the dependency chains in the parsing, so you want to use as long windows as possible.