Because the current requirements are constant and not like a photography flash just a short but extreme amount. There's no point in putting a few Watt seconds into a capacitor if the power requirement is 2kW for minutes.

Plus

• power storage is large
• you need a way to transfer the stored power into the water faster (otherwise why bother), which means thicker coils and more wear

For AC power, capacitors don't effectively store energy for later, and would change the power factor to make the resistive load reactive which can bring down the efficiency of the power transfer. For AC power a big ol resistive heater is probably as efficient as you can get, which is part of why those kettles are so simple and boil water so fast.

A kettle that stores energy would need to use DC power, converting it from AC and probably have a very large capacitor, more likely a battery.

because we unplug ours when we aren't using it, and capacitors discharge when not under current.