John Goff has set off a round of "what if..." Now Mr. X is at it.
The big problem with companies like Masten Space Systems, or Armadillo Aerospace, or SpaceX for that matter, is that they all have to design and build rocket engines before they even start on the curve towards cost-effectiveness. The engine is the single biggest piece of design risk on a rocket. It takes the most time from project start to operational status. It is, for the most part, the cost of entry into the space race.
When the Apollo program was shut down and replaced by the Shuttle, the U.S. already had the engine it needed for a big dumb booster: the F-1. This was a fantastic engine: it ran on the right propellants, it was regeneratively cooled (and so reusable), it's turbine ran off a gas generator (so there were no fantastic pressures involved), it had excellent reliability (some test engines ran for the equivalent of 20 missions), and it had respectable if not stellar Isp. By the time Apollo 16 launched, the F-1 was a production-quality engine.
The Saturn V was, however, way too big for unmanned payloads. It did not make sense to keep building these monsters. But a rocket powered by a single F-1, with a Centaur upper stage powered by two RL10s, could have put between 30,000 and 45,000 pounds into low earth orbit, about as much as an Atlas V lofts today. In fact, such a rocket would have essentially been an Atlas V, only we would have had it in 1973, and it would have been built with two engines whose development had already been paid for, one of which was already man-rated, and the other of which was the most reliable U.S. engine ever built.
Alternatively, the J-2 could have been used for the upper stage. This would have had the advantage of already being man-rated, but the disadvantage of being overkill (expensive) for putting satellites into GEO.
This rocket would have served as a great booster, for decades. Over those years, the F-1 could have had a long cost reduction and incremental development program, just as the RL10 actually did. Within a few years it could have been man-rated (using two or three RL10s on the upper stage), and carried astronauts up to a space station. Without the ennervating Shuttle development, that space station could have been a bit more meaningful. Heck, without the Shuttle development, we could have had a new Hubble every year.
And, over the years, if it had made sense, we could have tried parachute recovery of those first stages and their valuable F-1s. In short, we could have spent the last three decades racheting down the cost of LEO boost, while spending a lot more money on stuff like Cassini.
And, of course, the beauty part is that with the F-1 production lines still running, the U.S. would have had the capability to build a few Saturn 1Cs. That's the five-F1 first stage from the Saturn V. In the mid-80s, NASA would have debated the cost of building the Space Station with heavy launch, or with the single-F1 launch vehicle, and my guess is they would have restarted the J-2X program and gone with bigger ISS segments.
Anyway, didn't happen.