A good analogy to a model railway capacitor discharge unit is the lavatory cistern. Here a small bore pipe delivers water at a limited rate of flow and fills or charges up the cistern. On operation of the flush mechanism, a large amount of water discharges rapidly, executing its primary function.
For the simplest form of model railway CD unit all that is required is a capacitor and a resistor. When power is connected the capacitor charges via the resistor up to the peak value, not the average value, of the supply, usually about 22 volts. On operation of a point button or switch the energy stored in the capacitor operates the solenoid. If the button is held operated, the current through the solenoid is limited by the value of the resistor thus preventing the melting solenoid syndrome. The advantage of using an AC supply is the higher peak voltage as the energy stored in a capacitor is proportional to its capacitance but is proportional to the square of the voltage. With this simple unit there is one downside however, because of the resistor, the unit will take time to recharge, just like the water cistern.
The solution to much reducing the time delay is to venture into solid state technology using a power transistor. The transistor is used as a switch to disconnect the output if any buttons are held operated. On release of the button the capacitor charges directly from the supply and is ready for use very quickly. The green LED indicated power is on and the red LED indicates a button held in the operating position. On disconnection of the power supply the unit will automatically self discharge saving you the treat of getting a surprise bite from the capacitor. Commercial purchased units may be limited in the number of points that can be changed simultaneously therefore a custom built version can be made to provide extra energy.
Buying the few components is not expensive and remember you only have to build one of them for your whole layout.
Do you want to change even more points simultaneously? That's for next time.