The only time a larger pressure tank will help, is if you have a lot of long term uses of less than 1 GPM, which is rare.
As with your description of the kitchen faucet filling a one-gallon jug in 40 seconds, that is 1.5 gpm. This much flow would keep the pump running continuously, so the size of the tank doesn’t matter. If you don’t open the faucet all the way, the gallon of water in the 4.5 gallon tank will last much longer than 40 seconds. Even if you only open the faucet to ½ of a gpm, the gallon in the 4.5 size tank would let your pump stay off for two minutes, and run for two minutes, which is still better than you are getting now with a larger tank and no CSV.
One gallon stored in the 4.5 gallon tank lets your ice maker fill, or you can rinse a toothbrush without the pump having to start. Running more water than this like with a shower, garden hose, or filling a washing machine, a larger tank won’t help. The pump will still have to come on, even with a tank that holds 12 gallons of water, because you will use more than 12 gallons.
The theory is that the CSV saves so many cycles for things like showers and garden hoses that run for long periods of time, that it doesn’t hurt for the pump to cycle each time a toilet is flushed by itself. Then there is the fact that a toilet is rarely flushed all by itself. If the shower is turned on or hands are being washed within a minute of the toilet flush, there is no extra cycle just for the toilet. Even with the small tank on a CSV system, the pump usually comes on and stays on in the morning until everyone has showered and gone to school or work. Then it may come on and stay on for a while in the evening when everyone is home using water again. But during the times when few or no people are at home, it only comes on occasionally for things like the icemaker.
