Well, sure, but that only pushes the question back one step further: who told you which action to pick? Why pick R and not R^2, for GR, for example?
[ Just to avoid someone spending too much time on an explanation IAAPhysicist; yes I understand effective field theory and the preference for Lagrangians built from relevant/marginal operators. ]
The Navier-Stokes equations can be derived from the Boltzmann equation by applying a slight perturbation, expanding the result as a series, and taking the moments.
Taking the moments is essentially an integration, which comes with the implicit assumption that the system you're describing has sufficiently many particles. When running low on particles, this integration does not make sense. This is why the resulting equations do not apply at low densities.
The Navier-Stokes equations are the second order expansion of this procedure. The result of the first order expansion are the Euler equations.
This is called the Chapman-Enskog procedure. It's really quite illuminating when you see it for the first time. There's a great derivation in [1] if you can get your hand on it.
When I saw this derivation during a course Theoretical Astrophysics it was indeed very enlightening, what is interesting is that it easily generalises to magneto hydrodynamics and other more complicated situations (mixture of multiple different fluids, fluids that react with each other etc.). I believe Landau Lifshitz contains some of them.
I'd like to point out that space is an extremely large and harsh environment. The three main issues:
1) Distances are huge. Light needs ~5 hours to travel from Pluto to Earth. This means high-gain (=large), directional antennas, and low data-rates to make sure you actually receive the same data that the craft transmits to you (and vice versa).
2) Electronics need to be shielded from radiation and cosmic rays. On Earth, the atmosphere does a this for us (and we still get hit by cosmic rays, leading to things like randomly flipped bits). If you have a space-craft that cannot be directly controlled from Earth (because, 5 hours one-way communication time), you need it to be somewhat autonomous. Random bit-flips can spell disaster, so you need to either bring a ton of shielding, redundant (and well-tested, aka "outdated") systems, or both.
3) All these things add mass to your vehicle. Mass is the single largest cost driver in launch operations.
In summary, space is difficult and expensive to get to and operate in. This costs money. Money is finite, especially in a world where many people would like to see space exploration funding cut because it provides no immediate tangible return.
There's an additional caveat that may be of interest.
If you execute code in parallel, you may pick up different round-off errors unless you take care to combine the results from parallel tasks in the same order every time.
This can be a problem when simulating non-linear dynamical systems (such as the Solar System).
I'd like to point out that large-memory/many-core multi-user machines are very much alive in Computational Science (Computational Physics, Computational Chemistry, etc). Usually as test-beds (before deploying on clusters), visualisation system, or simply front-end nodes for clusters.
Simulations may run for weeks or months on large computing clusters. People wanting the resulting data may not have suitable access and/or resource allocations to repeat the runs.
https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_actio...
https://en.wikipedia.org/wiki/Electromagnetic_tensor#Lagrang...
Enjoy!