This blog post1 identifies the two main sources of inertia within the power grid:
- "Classic" generation, typically steam turbines
- Large industrial motors
Your understanding is correct in that overall system capacity is comparablecomparably low and provides a negligible effect to the system inertia.
From a reliability perspective, system inertia is a good thing. The large rotational mass providing system inertia slows the decline in frequency should there be a sudden change in the generation or load of the system. System inertia helps prevent protective load shedding mechanisms from kicking in by providing time for compensating control systems to adjust generation to the changing environment.
Inertia has become a greater subject of interest as newer renewable generation technologies have increased their footprint on electric grids. Newer renewable technologies connect their generation source to the electric grid through power inverters which do not provide any inertia to the rest of the system. Likewise, renewable technologies are enabling the retirement of older generation technologies which results in less system inertia being available. This decline in inertia is compounded by a decrease in large industrial motors.
1Please note, this source is a bit biased as they sell a product related to grid inertia
This presentation goes into some of the details regarding how system inertia is calculated.
Mechanical dynamics are modeled by the second-order differential equation:
$J\frac{d^2\theta}{dt^2}=T_m - T_e$
$\theta$: angle (rad) of the rotor with respect to a stationary reference.
$J$: moment of inertia.
$T_m$: mechanical torque from the turbine.
$T_e$: electrical torque on the rotor.
From there, you would need to sum the inertia provided by all of the major contributing sources. This is obviously a non-trivial exercise as generation schedules vary as do production schedules for large industries. You also have to take into account the preferred ramp rate of the generators which will vary based upon fuel source.
To provide a negative answer to your question - I think it's these aspects that makes it so hard to discuss system inertia in a quantified manner. There are too many variables and the environment is dynamic. You could perhaps identify the inertia for a small region, but certainly not for the region of a typical balancing authority or at a national scale.
Some concluding thoughts:
The pessimist might argue that system reliability is doomed due to the decrease in overall system inertia and that we'll see more brownouts and blackouts as part of upgrading the overall power grid.
That outlook is likely a bit too bleak though. Balancing authorities can require that more spinning reserves be available, which can provide fast(er) response generation for localized imbalances within the grid. Likewise, national level energy committees can provide compensation in the arbitrage market for fast voltage and frequency providers such as grid scale bulk electric storage systems (BES).
Obviously, those changes won't come for free - it takes fuel to provide spinning reserves, and grid scale BES aren't cheap. But the challenges are surmountable even if decisions have to be made based upon empirical evidence.