  We establish a general implementation-independent approach to assess the
potential advantage of using highly entangled quantum states between the
initial and final states of the charging protocol to enhance the maximum
charging power of quantum batteries. It is shown that the impact of
entanglement on power can be separated from both the global quantum speed limit
associated to an optimal choice of driving Hamiltonian and the energy gap of
the batteries. We then demonstrate that the quantum state advantage of battery
charging, defined as the power obtainable for given quantum speed limit and
battery energy gap, is not an entanglement monotone. A striking example we
provide is that, counterintuitively, independent thermalization of the local
batteries, completely destroying any entanglement, can lead to larger charging
power than that of the initial maximally entangled state. Highly entangled
states can thus also be potentially disadvantageous when compared to product
states. We also demonstrate that taking the considerable effort of producing
highly entangled states, such as W or $k$-locally entangled states, is not
sufficient to obtain quantum-enhanced scaling behavior with the number of
battery cells. Finally, we perform an explicit computation for a
Sachdev-Ye-Kitaev battery charger to demonstrate that the quantum state
advantage allows the instantaneous power to exceed its classical bound.
