MW batteries, page-85

Could be, but also hammering the batteries very hard could impact longevity/capacity.

Tesla's grid-scale products also seem to have similar power to storage capacity ratios:

The original Powerpack (used in the Hornsdale battery) could deliver up to 130 kW from its 232kWh storage capacity which is not all that much faster than the Powerwall's peak (not sustained) output of 1 kW of output for 2 kWh of storage capacity.

The newer Megapack seems to be the same ratio - "Each Megapack comes from the factory fully-assembled with up to 3 megawatt hours (MWhs) of storage and 1.5 MW of inverter capacity".