In most Hamiltonian and Lagrangian formulations, we use Canonical momentum and not just the momentum, which is slightly different.
Momentum and position (or p and q) are implicitly related to the Hamiltonian of a system, while force itself is dependent on the rate of change of momentum. Momentum is a more fundamental quantity rather than force and energy.
There are also cases where a body can have non-zero momentum and zero force, or vice versa.
Also, as you move towards quantum mechanics and relativistic mechanics, momentum becomes much more important. For instance, the Heisenberg Uncertainty Principle also relates position and momentum of a body, while energy is related to time.
And momentum is fundamentally linked to energy, and not force.
There are also cases where a body can have non zero momentum and zero force or vice versa .
In this statement can you explain me vice versa case by giving one example.
In Physics, any quantity we define must have some physical significance. Momentum is a fundamental quantity as it describes combined action of mass and velocity. It actually helps us to understand the individual contributions of mass and velocity to the impact made by a body. It’s also one of the fundamental constants of motion. The previous answer also carries its huge importance. And if you are still not satisfied, ask yourself this simple question
“We have velocity and time, then why do we define length?”