Laffitte is nice here, because the BBP might not trust York fully.
The BBP have no proof York is really on their side, IMO, and want to play this safe. If York is on their side? Great. If she's not?
Let's say York plans for Laffitte to free her, then to use the Seraphim to take over the Blackbeard Pirates and rule them (we know she's a greedy girl, after all).
Laffitte can use his hypnosis to fully make York and possibly the Seraphim under his control. Any chance of York betraying them goes out the window, and, now that Catarina has touched Saturn, York is no longer in control here.
If York was freed, but controlled the Seraphim still, she could control the situation here. The laser grid is still up, and she'd have to take out Laffitte, Zoro, Lucci, Edison, Usopp, Nami, and Chopper with the four Seraphim, probably taking out Laffitte, then Zoro and Lucci, then the rest. York would still be in a great place.
By gaining Command Authority over York through Catarina touching Saturn, and then hypnotizing York, the Blackbeard Pirates can guarantee York has no ability to betray them.