To allow public access to orbit, we would need breakthroughs that would lower the cost by a lot more than an order of magnitude and increase safety by a factor of 100 as compared to every launch system used since the first manned space flight. I think airborne launch will be a significant part of the safety solution. Breakthroughs to do the rest of the job are unknown.
Just my opinion, and two cents here, but the problem may be that too much is expected from a single launch system. If the Stratolaunch, or Birdzilla as some call it, can solve the safety problem, then some other technology can solve the other problems.
Spacex will most likely attempt to make Birdzilla launch platform fully reusable, which will help with the cost problem.
As for the rest of a comprehensive solution, you can look at other systems to help with costs from LEO on outward. For example, Quicklaunch can get materials into space cheaply. If feasible, a LOXLEO system can skim atmospheric gases from LEO and use it to power spacecraft after achieving orbit, while reducing costs still further. By combining these two systems, you could leverage a small payload of hydrogen from Quicklaunch into much more by using a LOXLEO system. Once you have the water in orbit, you can then split it into hydrogen and oxygen. This could support missions to cis Lunar space where the moon can be further exploited into a base for interplanetary exploration and development. Thus, not all of the requirements needed will come from one system, but a series of systems.