This implementation is much easier than your shift register proposal, it's almost trivial.
I thought so, but as always, I was thinking about "n" LCDs, not 2 LCDs 
I think it's the matter of which solution will save more pins for other purposes. The shift register, AFAIR uses three pins, so in case of small number (1 to 3) of LCDs it's of course more "economic" to use one more pin for every LCD. Thanks.