As far as I can tell and have heard other people much smarter than me say, there's no real physics-level barrier to any of Starship's goals. There's plenty of tough, tough engineering problems to solve, but it doesn't require unobtanium in order to work.
SpaceX has already pulled off landing an orbital-class first stage (not to discount the prior work in the form of DC-X and others, but they weren't orbital), and they've gotten to the point where they can refly those stages many times in relatively quick succession. Seems reasonable to believe that they can figure out Starship, even if it may not be in the exact form or on the exact timescale that they want.
NASA has invested more than SpaceX in the Space Launch System (think $20B plus in spending). This will be a rocket that is disposable, every launch it lands in the ocean, all work lost. Estimated per launch costs and sustaining costs for all the facilities involved run about $2B-$3B - NASA isn't saying actually.
Anways, once things are head to head we will get to see if Musks promise of cheaper access to space vs the rocket with tons more money invested pans out.
Facility List for SLS by the way to give you just a sense of the cost base Musk is competing against.
Booster Fabrication Facility (BFF) - 45-acre site at KSC used to refurbish, manufacture, and assemble the aft skirt assembly and forward assembly for the SLS boosters. Includes the Multi-Purpose Logistic Facility used to receive, inspect and store shipped flight hardware.
Vertical Assembly Building (VAB) - Large (456 ft H max) vertical rocket integration facility. Floor load capacity of 12 million lbs, cranes located throughout building. Handling and storage of hazardous/ nonhazardous commodities.
Payload Hazardous Servicing Facility (PHSF) - The Payload Hazardous Servicing Facility (PHSF) was built in 1986. It is a Level 4, class 100,000 clean room that can be used as a Payload Processing Facility (PPF) and/or a Hazardous Processing Facility (HPF).
Michoud Assembly Facility (MAF) – 832 acre production complex located in New Orleans. MAF is one of the largest manufacturing plants in the world with 43 environmentally controlled acres (174,000 m2) under one roof. Includes two Vertical Assembly Buildings. Current site of the majority of core stage manufacturing and assembly and planned location for EUS manufacture and assembly.
Systems Integration Lab (SIL) - The Systems Integration Lab (SIL) supports end-to-end integrated avionics and software integration, check-out, verification, and validation. It demonstrates real-time flight control of a launch vehicle, such as SLS, during ascent. This lab at NASA’s Marshall Space Flight Center in Huntsville, Alabama, not only includes the flight computers and avionics identical to the core stage avionics but also includes emulators for the rocket’s boosters and engines, the Launch Control Center and Orion.
Systems Integrated Test Facility (SITF) - The Software Integration and Test Facility (SITF) at MSFC on Redstone Arsenal integrates and tests software specifically for the SLS Core/Upper Stage avionics system.
Software Development Facility (SDF) - This Capability Maturity Model (CMM) Level 3 certified facility at MSFC performs a complete range of flight software activities from requirements development and analysis, software processes and planning, design and development, to systems integration and development testing. Products developed at the SDF are installed and tested at MSFC’s SITF.
Huntsville Operations Support Center (HOSC) – At MSFC on Redstone Arsenal, the HOSC is capable of distributing secure mission voice, video and data anywhere in the world. Includes Engineering Support
SLS Engineering Support Center (SESC) - Engineering Support Center (SESC). Certification runs for contingencies are performed by engineers responsible for the major elements of the SLS. Located in the HOSC, the SESC leverages remote architecture built for the ISS Payload Operations Center to allow engineers to focus on the engines, boosters, and stages of the SLS during testing and launch.
Advanced Manufacturing and Weld Facility – Located in MSFC’s Building 4755 on Redstone Arsenal, this friction stir welding facility uses advanced robotic tooling to weld barrel or dome segments up to 33 feet in diameter.
MSFC Flowrate and Structural Test Stands –Located at MSFC on Redstone Arsenal, designed to push, pull and apply pressure loads to SLS cryogenic tanks. Cutting-edge technology is also adaptable for future large-scale rockets and systems. Testing and data can be safely monitored from a control room via fiber optic cables.
Stennis Space Center – Multiple propulsion testing facilities for components, engines and stages located near Bay St. Louis, Mississippi. Facilities include the B-2 test stand used for the SLS core stage green run. Formerly used for Saturn V and Space Shuttle testing, this stand is equipped with a 195-ton (US), main derrick, lifting crane, with a 20-ton jib crane and is capable of static-firing test articles up to 33 ft in diameter.
So for example if it’s not as cheap as expected, it’s still huge that it can deliver volumes larger than the interior of the ISS to orbit in a single launch — that alone means much less of a need to resort to exotic materials and expensive engineering to cut down on weight and volume on projects like the James Webb Space Telescope. It could also have huge implications for which types of orbital stations it’s practical to build.
SpaceX has a good track record of success with their rockets and with this project in particular. They seem to have the skills and backing to make it work, and they aren't discouraged by setbacks. Of course it is not guaranteed to succeed, but it seemed clear to me that the point of this article was to explore what could be done with starship if it does succeed.
Starship seems to, again, require a few of these X% improvements. And the thing about exponential growth, as Covid kindly reminded us, is that eventually it is overwhelming.
So I don't think you can simply extrapolate from "they have a good track record of solving hard problems", because the problems they tackle are getting harder and harder.
I wish them well, but I'm tired of all these blogs writing about Starship as if it's a done thing, to the point of writing about delivery costs. It might happen, it might not.
The typical solution, which is in the context of relighting a liquid fueled rocket that is coasting in microgravity, is to use some other engine to push the fuel in one direction, providing enough initial ullage to light the main engine after which the thrust from the main engine provides the rest.
For refueling it is normally assumed that the target and resupplier are stationary when docked, or at least not accelerating to their next set of orbital parameters; they are station-keeping. The typical solution doesn't work there, so there is research to be done on just how the refueling will work in practice.