If you want to do dynamic positioning, then you must take into account the load vs. motor inertia. With a perfect match, the load and motor inertia are almost equal.
Note that a pancake motor has higher torque but lower nominal speed as radial motor. It has also much higher moment of inertia.
A radial motor is often used with combination of gearbox, so you can match load and motor inertia. The transormed load inertia is then J'=J_load/p^2 where p is the gear ratio. So you can have high dynamic system using a low inertia motor with high reduction ratio gearbox.
A pancake motor meanwhile is more suited for applications where gearbox is not needed, but you need a high torque and low speed. These applicationa are typically direct drive, gimbal, ...high inertia load. It has also a possibility to have a hollow shaft, where you can put slip rings to supply sensors, other devices mounted on gimbal.
Now, what importance has the load inertia and what does it do?
Every mechanical setup has its own elasticity, like torsional elasticity. Having numerous axes, gears,...means that a load is spring like attached to the motor. We call this torsion spring. Now we have a rotor that is coupled by this torsional spring to the load. This system would have a resonance and an anti-resonance frequency. If the load and rotor have the same inertia, then those two frequencies are identical.
If inertias are mismatched, then you get a lower resonance frequency, which means it is harder to filter out, the whole system has to be tuned to a slower dynamics to stay away from this resonance which has to be damped.
Another resonance link
Let we have a radial motor with mounted encoder or brake, the rotor inertia now becomes the sum of all inertias: rotor + encoder + brake. Why? Becuase they are stiff mounted on rotor and no elasticity is between them. So now we have altered the motor rotor inertia. Anything on rotor, that is rigidly coupled becomes a part of rotor, not a load.
With a pancake motor, we could say that the mechanical setup is almost perfect, if the rotor is stiff mounted with a load. Therefore you get only one main natural resonance frequency that will determine the maximal dynamics of the system. This is one main advantage if you want a high dynamic system.
A closed loop system like servo , prefereably has to have low response time aka high dynamics. This can be acheived with increasing the overall gain - loop gain, by increasing controller proportional gain. Now, if you look at the Bode plot, you can notice that at node, the system has a considerable gain and yet more important, it has a phase shift of -180 degrees. That means, the system will begin to oscillate exacty at the resonance frequency. So, when tuning the servo, the gain has to be such that there is always a safe margin, to remain stable. As the node gain is smaller and it has higher frequency, the system can have more gain and thus have more dynamic response. The last way to improve the dynamics is to add low pass filter, notch filter,...If the rotor is stiffly coupled to a load, like for example a gimbal, we get a neat high resonance frequency that can be elliminated by inserting a notch filter.
Therefore, yes the inertia is very important for closed loop servo sytem due to these resonance nodes.
Refeerence - Siemens S120