Flywheels store energy. This energy can be unloaded very quickly as opposed to waiting for a power stroke from a piston. The faster the flywheel is spinning, the greater the rate of energy delivery to the load.
Peak power demands by a large load... Say a big induction motor on an air compressor can be extremely hard to start without a flywheel system. In order to start these kinds of loads, you either need to oversize the engine and the generator head, or you add flywheel mass. From an expense point of view, the cheapest place to add flywheel mass is on the generator head.
It is my view that the Lister orginal equipment, such as the SOM, were underated. These engines were really designed to serve industry. I do not have a 6/1, but it is my understanding that they can output 3.8kW continuous. Peak power on something like that can exceed 5kW for a very short period of time... Initially the load would be served by the flywheel, then the rack would open up.
Heavier flywheels permit higher peak power to be delivered. Faster spinning flywheels permit the power to be delivered at a faster rate.
Continous power is the rated HP output of the piston. Peak power is the rated HP output of the piston, plus the stored energy in the rotating mass: crankshaft, flywheels, generator rotor, and any additional masses such as pulleys or shafts.
I am currently designing a jackshaft for PTO from an engine system. The jackshaft will rotate at 1800 RPM and permit direct coupling of the generator head. The rest of the high speed shaft is available for mounting flywheel mass and for additional PTOs. Because of the higher speed, I am planning on boring and milling out junk steel flywheels from trucks and tractors and stacking them on the keyed jackshaft. This shaft will not increase the total horsepower, but the peak power would be increased dramatically, as well as the peak power delivery rate... Because of the stored energy in the shaft. Hard to start motors and other loads with high torque requirements can be started in many cases before the rack has a chance to respond.
One of the problems with having a generator without a flywheel in the system is with starting big motors and air conditioners, especially capacitor start electric motors. The generator may have a continous output rating sufficient to run this type equipment, and still be unable to start it. This really tears up the motor because they get very hot quickly if they are not brought up to speed rapidly. The commerical equipment that does not use flywheels get around this by running the engines and generators at higher speed, usually 3600 RPM. The increased shaft speed increases the delivery rate and makes starting big loads a little easier... But even at 3600 RPM, most generator set are not going to have a great deal of peak power available because they lack flywheel mass.
Another way to look at this is compare a Lister type engine with a gas or diesel modern engine running at higher speed, but with the same HP rating. The modern engine will have a faster delivery rate, but the Lister type will have greater peak power due to the flywheels. If you look at the SOM you will see the orginal equipment has added flywheel mass on the generator pulley. This provided an increase of peak power, and in delivery rate.