The use of the Lagrangian is not due to Gell-Mann but to the introduction of this method by Feynamn towards the end of the 1940, to make calculations easier with the QED method, itself established from QFT.

Also, there is more to the physics of particles than the Standard Model. The Standard model is fundamentally only a list of particles.

You would learn more about particles if you investigated how each one was discovered.

If you could locate an old copy of "Physics" by Halliday and Resnick, or "University Physics" by Sears, Zemansky and Young, you would connect with the true basics of physics.

I think you have in mind the Hamiltonian formalism as in Classical Mechanics. In fact, it is possible to formulate the Standard Model in terms of a Hamiltonian formalism. Even, Hamiltonian one is more convenient to introduce the quantization. However, Lagrangian is more convenient to discuss Lorentz invariance and related converved quantities.

In this case, Gell-Mann was the only man who could construct and see really the 3 Quarks in a simple picture; all others have to imagine the "Standard Model" as formulas which nor can be seen nor be real.