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 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.