Hmm, okay so if it's because of a future card interaction, then if we assume its manipulating Agenda or Power counters then there are a few options:
1) Move Agenda not Power counters: Jinteki can move counters between Braintrust, Nisei, and HoK, but not LS. Maybe they don't want to load LS up with too many counters, but this doesnt really make sense since Nisei and Braintrust are both waaaaay better with the abundance of counters from HoK (not to mention Astro Beale), and HoK is a far more efficient battery for counters than LS is.
2) Move Power not Agenda counters: LS can be loaded up with counters from Draco (possibly the best power counter battery since you can choose an arbitrary based on whatever you want to pay), but you still have to score a 5/3, the ability has limited use, and there are far better things to move them to (Data Raven, Mamba, Victor 2.0, hell even Snoop)
i cant really think of anything else, neither of those seems to be a good enough reason for the difference