How are you defining "slow" in this comment?

My understanding is that batteries are demonstrating longer useful lifetimes than was anticipated.

Ultimately I think diversity in technologies is the best policy, but difficult to set up the incentives to achieve it.

Both assertions are false. Batteries react within milliseconds [1], and last 10-20 years (depending on chemistry and cycling, lithium at the shorter end, sodium and flow at the longer end) [2] [3] [4]. Australia had to reconfigure its ancillary services market due to how fast battery storage reacts, for example (proven out with the Hornsdale Power Reserve).

Please update priors to current state of the art.

[1] https://www.eia.gov/todayinenergy/detail.php?id=50176

- The most common cited use case for batteries is frequency response. Frequency response is a service that maintains grid frequency as close to 60 hertz (Hz) as reasonably possible. Deviations below 60 Hz can lead to protective generator trips that result in a subsequent decline in system stability. Batteries are particularly well suited for frequency regulation because their output does not require any startup time and batteries can quickly absorb surges. At the end of 2020, 885 MW of battery storage capacity (59% of total utility-scale battery capacity) cited frequency response as a use case.

[2] Smith, J. et al. "Lithium - ion battery degradation mechanisms and mitigation strategies for utility - scale energy storage". Journal of Energy Storage, 2020.

[3] Brown, A. "Lead - acid battery performance and lifespan in utility - scale applications". Power Systems Research, 2018.

[4] Green, C. et al. "Flow batteries for long - term utility - scale energy storage: A review". Energy and Environmental Science, 2019.

If the washing machine is using an induction moter, the capacitor is for creating the conditions for it to self-start on a single phase system. Three-phase induction motors don't need this.