There is debate on this, and in my opinion those who claim increased speeds are saying that to sell more products.
My opinion is the cap pack provides ripple voltage protection to reduce stress on the esc. I personally (have an EE Degree) do not believe that a setup of parallel capacitors can provide any amperage benefits worth noting. I do believe they help smooth out oscillations and that high quality batteries also help.
Charge up a cap pack and connect it to something and you can see. It does not have the power to run a 40mm brushless motor for even a second.
Castle ESCs are the ones that seem to need cap packs or they will burn up. For whatever reason the HW ESCs can take the abuse of ripple voltage better.
There is no real debate to be had on this. You are 100% correct. Anyone who says that besides smoothing there is also a performance advantage to using cap packs, either has no basic EE understanding... or must have a financial interest vested in them, to lie.