Because you can bias the process to be more likely to represent data relevant to your domain.
Note: I'm not in any way a compression expert, so while it may be obvious to you/others, it's a little interesting for me to think of compression in this way (sending parameters to a shared process, instead of sharing the raw data).
Then, "referencing a region" of the state is basically the same as just giving the value. The nth value is just n itself.
So clearly that doesn't give you any advantage. Why would randomizing the data sequences make it any more efficient on average?
Although if you specifically choose the ordering of the sequences so that common sequences are easy to represent and uncommon sequences are hard to represent, then you basically have Huffman coding/arithmetic coding.