Economic advantages? Sure, for the DropShip captains. I'm not so sure there are economic advantages to be had for the JumpShips, though. Not unless the JumpShips and DropShips are owned by the same entity, which probably won't be the case.
One economic advantage is that since you are orbiting near the planet instead of at the Z/N region, you are 1/10 the distance to the sun, meaning you can receive up to ~100 times as much solar energy per square meter. This means your recharge time can drop to as little as 1% normal. However this imposes all the quick-charge penalties associated with doing that. Still, if the star you are targeting to jump to has a 300 hour recharge time at the Z/N zone, and you need to shave hours, jumping to a pirate point (i.e. between the planet and the star) means instead of spending 300 hours recharging, you only ned to spend ~175 hours (or whatever the safe recharge time is).
It also drops time for Dropships to transit. IIRC, it is on average ~10 days transit to/from Z/N and the destination planet, but only ~8 hrs from a pirate point to the same planet. So instead of your Dropships burning fuel for 20 days, you can deliver cargo within 20 hours.
Even if there were no safety and filling-up-space-available-docking-collars aspects in favor of Z/N (and I feel it's pretty well demonstrated that there *are*), keeping insurance coverage is surely an economic disincentive for a JumpShip owner in making repeated use of pirate points. I'd even imagine insurance concerns might limit commercial JumpShips from using anything BUT Z/N points (barring of course those times House Armies shanghai the ship into military service).
Insurance would raise rates for using Z/N points, but if the Jumpship can travel faster due to using them the insurance costs can be handled by having higher income. You are also only ~8 hours away from an inhabited planet, instead of ~10 days, meaning if you get in trouble you can get helped a lot faster.
Yes the drives are powerful, I was thinking more the combined time to charge the drive and get to a new pirate point. I don't remember if a jumpship can effective use its drive to maneuver and keep the jumpsail deployed.
For the planet-star pirate point, it is effectively the L1 LaGrange point which objects can orbit (like
SOHO is). So a Jumpship could jump to the L1 pirate point, maneuver into a parking orbit, and deploy its sail partially (due to the 100* as strong solar emissions at that distance).
Now the fun part for the L1 point is that it incorporates rotation of the planet as part of the math that defines the L1 point, but a pirate point is only concerned with gravity. So that could make things 'interesting'.
(This Pirate Point discussion is why one of the supertechs I wished the WoB had developed was a Pirate Point Network. I.e. a freighter wants to go from system A to System B, but reduce travel time. So they pay a fee to WoB, and request pirate point calcs from the local HPG. That HPG sends a request to the destination system for current pirate point calcs. The destination system processes the calcs and includes a time frame where those calcs can be used, and a second time frame where they will be useless. This is to make sure nobody tries to jump in at the same time someone else is maneuvering to leave. System B HPG sends the data back to System A, and System A sends the calcs to the requesting Jumpship. Each system's HPG uses its own HPGs supercomputers to calculate continuous pirate point calcs in case they are needed, both for the main planet, and for other planets in-system. It would allow rapid freight shipping, and also rapidly deploying troops from one planet to another.)