Or perhaps your understanding of the problem is incomplete?
The point of the batteries are to store power when it's cheap and abundant, then deliver it during peak demand for sustained periods. The time between those periods is measured in tens of hours.
Of course we care about the energy amount stored - some. But total power capacity is more important for a large number of applications.
The usage the OP listed (arbitrage) is only one of the 9 function listed by the National Renewable Energy Lab[1]. Many of the functions need immediate power capacity in the seconds to an hour (so MW seconds or MW minutes), and more important is the speed of response and the amount of power deliverable.
The point of the batteries are to store power when it's cheap and abundant, then deliver it during peak demand for sustained periods. The time between those periods is measured in tens of hours.