But for a bit more outlandish plan: Let's launch the vehicles from a platform in 30km altitude to almost completely eliminate the atmospheric drag at launch. If ChatGPT is right, 130t of helium would suffice to offset the 5000t of a fully loaded starship. Helium costs $100k/t, so for the mere starship weight we would need $13million. Make that $130million for a full 350 million cubic meters zeppelin/balloon/structure - costs of the order of magnitude of a single launch to LEO. At that altitude, winds are below 120km/h and drag less than 2% of an equally strong wind at sea level.

How can we anchor a lighter-than-air platform of that size? It's size would be equivalent to a sphere with a radius of 440m - almost 900m across, so quite a mega structure. But a balloon or zeppelin shape would probably be the best, with the platform hanging below it. The rocket could dangle below it and enter into free fall before igniting the engines. It would lose as little altitude as necessary to safely fly around our platform. No trouble with blown up concrete at the launch site. The anchor site could be a single site so the zeppelin would align with the wind direction but the tether would need enormous tensile strength and provide for transport of parts, liquids, gas, data, electricity and ultimately humans.

Catch at 30km or on the ground? I think, once it works well, returning boosters could be caught below the zeppelin again. Maybe not too close to not lose that mega structure but the maneuver would be quite similar apart from the zeppelin not having a static geo location and the booster needing to go a few meters sideways in the final approach.