Answer: No, it doesn’t make sense.
A Skyhook's center of mass orbits at (roughly) half the altitude of the point for pick-up of descending cargo. The altitude of satellite constellations in LEO orbit is low enough that atmospheric drag de-orbits them within a decade of decommissioning. This means the skyhook (at a much lower altitude) would experience higher levels of drag and de-orbit itself even sooner.
There is a large mis-match in velocity between the cargo and the pick-up mechanism due to both the difference in orbital altitude and the rotational velocity of the pick-up on the end of the rotating tether.
Also, skyhooks are limited to capturing download cargo with the same orbital inclination as the skyhook's center of mass. This is tricky when dealing with a dispersed constellation. The decommissioned satellite will need to match orbital inclination and right ascension of the ascending node, match orbital phase angle and accelerate to match the pick-up (which has higher velocity than circular orbital velocity at that altitude).
And the location of this rendezvous must occur so the satellite drops into the designated landing zone.
All very challenging for a "dead" satellite.
Even without the materials and deployment issues. “Given our current technological state”, this plan is not feasible.
