One major reason for this is the mixing plate at the top of the combustor. Fuel and oxygen are distributed to tiny nozzles which mix together. The better the mixing, the more stable the burn. If you get unstable burning -eg momentarily better mixing in one area- it will cause a pressure disturbance which will further alter the burning power in different areas of the combustion chamber. At low throttle, this can be enough to cause the engine to turn off entirely.
Fluid simulations have made a huge difference. It's now possible to throttle engines down to 5% because mixing is much more stable (manufacturing improvements in the nozzles have also helped) and combustion is more protected from pressure variations.
The extra stability also just makes it easier to control a rocket period. Less thrust variation to confuse with drag properties, less bouncing, better sensor data.
I guess I’m trying to connect the dots on how a simulation improves the actual vehicle dynamics.
Simulation inside the engine can find resonances, show where shockwaves propagate, and show you how to build injectors (pressure, spray etc) so they are less affected by the path of reflections. Optimizing things like that smoothly along a range of velocities and pressures without a computer is not very feasible, and you need a minimum of computing power before you start converging to accurate results. The unpredictability of turbulence means low-resolution simulations will behave very differently.
Modern pressure vessels can reach 5% empty mass, thats a factor of 20
Rockets have stages, a good approximate is to stage half your rocket to get rid of the most empty mass. This also means your first stage has to have double the thrust to lift itself and its stage. Now you're at a factor of 40 just to hover.
Now you actually have to take off, usually around 1.2 to 1.4 thrust to weight.
So a more realistic scenario means your rocket engine has to throttle down to exactly 2% power while the laval nozzle is optimised for takeoff thrust only.
SpaceX Merlin 1D: ~40% Rocketdyne F-1 (Saturn V): ~70% Space Shuttle Main Engine (RS-25): ~67% Blue Origin BE-4: ~20–25%
Falcon 9 does the "hover slam" where they have to turn off the engine exactly at touch down, or the rocket starts to go back up again. Throttle is too high for the weight of the booster at that point in flight.
So they need to "hoverslam", that is, arrive at the landing pad rapidly decelerating so that their altitude hits zero just as their speed hits zero. This was thought to be very hard, but I don't think SpaceX has lost a stage due to estimation failure there. It helps that there is significant throttle range and fairly rapid throttle response on the engines, so they can have some slack. (Plan to decelerate at 2.5g for the last ~20s or so, with the ability to do anything between ~1.5g to 4g, so you can adjust throttle based on measured landing speed.)
Their Superheavy has more engines, allowing them to bring the TWR below 1, enabling hovering.