I'm not familiar with sequencing economics, would you mind explaining the cost of a "run"?
Edit: this video may be able to explain a little better how this process works: https://www.youtube.com/watch?v=fCd6B5HRaZ8
New methods are already here, long read sequencing direct from source with minimal preparation . It doesn't say much about cost, but considering reduced preparation step and smaller equipment it should be a fraction of Illumina.
There are some interesting developments out there, like using enzymatic methods to synthesize long strands, but a lot of that technology is still in it's infancy.
I would be happy to discuss the field if anyone is working in it (or has interest)
Maybe sending data via rocket ship (since every ounce counts), when interception of signal is a concern (some reason to avoid using light)?
In theory, you could use DNA-based reactions to solve problems. Since DNA is quite small and the reactions run in parallel (more or less), you should be able to brute-force some otherwise intractable problems. The classic example of this is Adleman (1994), which uses DNA to find a Hamiltonian path. (here: https://www2.cs.duke.edu/courses/cps296.4/spring04/papers/Ad...)
In practice, anything involving DNA is a bit fussy and error prone, and exponential growth means you'll eventually drown in DNA too.
I don't see any DNA-based computing or storage systems as being capable of outdoing a general purpose computing system that already exists off the shelf, for the foreseeable future, for any reasonable use case.
Imagine the copyright strikes of storing (and replicating) all of YouTube in a teaspoon.