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. 

 Searching for this, all I can find is https://en.wikipedia.org/wiki/Rockoon where the balloon is lost with each launch.

What's the catch? Is such a cable not feasible? A 35km Zylon cable would weigh 50t to only support its own weight. Increase that cable weight budget by x20 to 1kt and it should still be little compared to the above example of 50kt of lift capacity. Zylon is commercially available at about $200/kg. For this project that would cost $200M. For a reusable rocket launch platform, that's still peanuts, right? 

 There have been many tether-based designs to bring stuff to LEO. It looks feasible on paper but it's an open question whether it would work in practice. It's certainly a lot of fun to imagine a world with these gigantic tethers.
There are many unsolved challenges:
a) to build it
b) to make it work, 
c) to make it cost-effective
And you can't only consider the costs of mass-to-orbit by starting from 30km altitude. You first need to bring your payload from the ground to that platform. All in all, it looks cool but the starship design is really at the frontier of what is currently possible.
Reaching 4% for SpaceX is not just having 1 killer feature that changes everything, it's rather the accumulation of a very significant number of small improvements regarding materials, strucutre, fuel, engines. 

 Ok, I spent way too much time these past days on this but I learned a lot.

I learned that my original assumption that atmospheric drag was significant to Starship was wrong. Some Wikipedia article quoted the drag loss with "1500 to 2000 m/s" while a Saturn V which is most comparable to Starship reduces this to a mere 40m/s on ascent.

I learned that there is such a thing as gravity loss. The idea here is that due to the atmosphere, the rocket cannot accelerate horizontally as would be ideal to quickly accumulate orbital speed. It has to start vertically and fly at a steep angle for a while, which contributes little to nothing to the orbital speed. All components that only fight gravity without adding speed are "gravity loss" and that is also quoted with 1534m/s for the Saturn V. With a high launch this could be lowered but by how much? A space nerd guessed 500 to 1000 m/s given the atmosphere up there is less than 1% of ground level. 1000m/s would translate to an extra 18 tons of payload to LEO per launch. According to https://aerospace.csis.org/data/space-launch-to-low-earth-orbit-how-much-does-it-cost/ that would be worth $27M per launch. 

 Getting to 30km height ideally costs just the potential energy and electric lifts are pretty close to achieving that, so it would be desirable to get out of thick atmosphere that way.

Is it possible with today's materials to build a blimp that can just float for years without needing a full replacement? I think it could be compartmentalized. If the blimp has individual chambers such that a sever damage in one point can be compensated by pumping gas to a different chamber while fixing that spot, while smaller damage gets repaired by autonomous robots, while using at least one redundant tether so you can maintenance or replace these, too, ... you could have the whole structure maintainable. Then it comes down to leakage cost and longevity of the materials.

If you have 50 launches per year, you get a life time budget for construction and maintenance of $1.35B/year. 

 Of course, with two launches per day, that budget increases to almost $20B/year etc.