For liftoff, you need tons of pure, raw thrust. F-1 was exceedingly good at that, despite it's rather low specific impulse. Solid rockets are also good at producing tons of pure raw thrust, but they have a lot of drawbacks as well-- can't be throttled (which in fairness basically neither could F-1) but most importantly, once lit CANNOT BE SHUT DOWN in an emergency. Solids are fairly simple, but INCREDIBLY heavy since they must be moved FULLY FUELED, or else stacked on the launch pad (as would have been done with ALL the Saturn V upgrades that involved adding solid rocket boosters to Saturn V). Liquid engines can of course be throttled (if designed to do so) and can be shut down in an emergency, and are more efficient for their propellant and stage mass than solids. ANYWAY, specific impulse, on a first stage, takes a back seat to two other design criteria-- maximum thrust for the size/weight of the stage, and maximum propellant density versus minimum stage empty mass. While solid propellants ARE very dense, their specific impulse is pretty low, and since the motor casing must withstand 700+ PSI of burning propellant gas pressure inside it, the stage then essentially becomes the combustion chamber, and is exceedingly heavy for its size. Liquid propellant tanks on a liquid fueled stage may be larger, but are very thin and lightweight by comparison, giving a much greater mass fraction between propellant mass versus stage empty mass. The key is minimizing dry stage empty weight (mass) versus loaded stage weight (filled with propellants). That is why kerosene and other denser liquid fuels are better for first stages than hydrogen, which is extremely "fluffy" and low-density by comparison. Yes hydrogen burns with higher specific impulse than kerosene, BUT due to its low density it requires absolutely ENORMOUS tanks to hold the necessary propellant to feed the engines for the duration of the first stage burn to get it to the altitude with the expected liftoff mass of the entire rocket. For instance, had M-1 been chosen for the first stage engines of Saturn V, it would have required a first stage at least TWICE AS BIG which would have made Saturn V 1/3 taller or so than it was. Any gains from greater efficiency of burning hydrogen would have been more than lost to the additional weight of the extra long tanks, which would have basically DOUBLED the weight of the first stage. Hence M-1 was never considered, and why the SLS is SO inefficient, and why Delta IV Heavy is SO big for its "medium" lift capability. That's why you want to use dense fuels like kerosene or hydrazine (in storable propellant missiles or rockets like Titan II) for first stages, or solid propellants (but again, storable liquids are more efficient). From this point of view, the first stage of C-8 is pretty reasonable and makes sense.
For upper stages, though, specific impulse becomes the overriding factor in performance, particularly for in-space stages like the S-IVB. This is why virtually ALL "high energy" upper stages use hydrogen as a propellant-- it has the highest chemical propellant specific impulse available without resorting to exotic fuels like hydrogen/fluorine, which was experimented with but never got outside the lab for obvious reasons... (liquid fluorine is about like handling liquid death-- hard enough to keep from destroying the lab or killing everybody; putting hundreds of thousands of gallons of the stuff in a FLYING ROCKET would be virtually suicidal...) ISP trumps all other considerations, with minimizing stage mass right behind it (or hand in hand with it). Minimizing stage empty mass is also a critical consideration. For instance, on Saturn V, every extra pound of stage mass on the S-IVB was a pound of cargo capability lost to the Moon. On the S-II second stage it was almost as bad-- every 1.1 pound of extra mass on the emtpy S-II stage was a pound of usable cargo lost to the Moon. For the first stage S-IC, though, you'd have to shave off ELEVEN POUNDS of empty mass to get an extra pound of cargo to the Moon... So you can see the weight becomes the biggest design driver for upper stages. You can use kerosene or even solid propellants for upper stages (as has been done on Soyuz, Falcon 9, and solids on many upper stages, kick motors, etc. over the years, including the Jupiter C rocket that orbited the first US satellite, but they're TERRIBLY inefficient due to the lower ISP and in the case of solids, empty stage mass for its size. That's why the solid upper stage on the Antares rocket makes so little sense, but then again, Antares is a "one trick pony" made just to loft the Cygnus cargo carrier to ISS to fulfill their COTS contract with NASA, nothing more. SO inefficiency is fine so long as it works. Falcon 9 would get a HUGE performance increase from a hydrogen upper stage, simply due to the increased ISP. So would the Soyuz rocket for that matter. BUT, hydrogen upper stages are a lot more complex and hydrogen is a much harder fuel to deal with... which means more expense. Both Soyuz and Falcon 9 are perfectly capable of doing the assigned job without the extra complexity and expense, so why bother. It's always an upgrade option if needed.
That said, M-1 would have presented some interesting design challenges and possibilities for upper stage use. It had VERY high thrust-- 1.5 million pounds. BUT you also have to either shut down engines OR deeply throttle your upper stage engines as you are nearing burnout of the upper stage. You have to do this to prevent overstressing your stage, any upper stages above it, and the payload/cargo with excessive g-forces as the fuel mass burns off but the high thrust remains, increasing acceleration exponentially. S-IC did this by shutting down the center F-1, while keeping the outer four burning until stage shutdown. The S-II J-2's were throttleable, so they throttled down to compensate for the empty propellant tanks as the stage neared burnout. So did the single J-2 on the S-IVB. M-1 would to have to be designed to be throttleable, in order to not overstress the rocket and payload near burnout. With 2 M-1's you could theoretically shut one down and just run on the other one as you burned off fuel, to prevent overthrusting the stack, similar to how the SN-8 Starship did in its recent belly flop test... shutting down Raptors one by one as the fuel was burned off in the stage. The rest is just control algorithms, programming, and dynamics. (Sort of how single F-1 powered Saturn IB proposals wouldn't have been that much of an improvement alone-- the 8 H-1's provided about the same level of thrust as the single F-1, so liftoff mass couldn't have been increased by much (therefore payload increase would have been negligible... now if you substituted a 1.8 million pound thrust F-1B in its place, as likely would have happened, then you get some decent increase, but the only other way to do it would be to use TWO F-1 engines on the first stage, but not being throttleable, the final 10-15 seconds of the first stage burn would require shutting one of the two F-1's down and continuing to stage shutdown on the single remaining F-1 to prevent overthrusting the stack and violating your g-load tolerances... you just have to switch the controls over so the single F-1 still provides all the control of the vehicle through stage shutdown... not an insurmountable problem.
ANYWAY, if you want to see the images and stuff I summarized from the studies I've read and gleaned over, search for "NASA study summaries" in the scale section of the forum here, or go over to the Sagitta Cantina forum and Bernie put them all in "Luke's Study" section there for me, as a resource for modelers to use for these little-known or unheard of or unrealized proposals that never actually got built... tons of good stuff in there! I need to get back to doing more of them actually... here's the link...
Later! OL J R