How can the same upper stage be optimal on a common core booster as well as on a single booster?

Question

Bundling three or five first stage cores together improves the launch capacity a great deal. But Delta, Falcon and Angara are supposed to use the same upper stage in their multiple common core versions, as their weaker single core versions do. They double or multiply the amount of mass they can put in orbit, so why aren't larger upper stages used for the common core versions of those rockets?

For example, if a Falcon 9 launches 20 tons of fuel to dock in LEO, how can the same upper stage be used to launch 40 tons of fuel to the same orbit? Doesn't it need to be larger and maybe sturdier to support the much heavier payload?

Similar with Atlas V that has a pretty wide range of capabilities using zero up to five solid boosters. But it always uses the same single engine Centaur upper stage.

Answer 1

You haven't defined "optimal" here. The commercial launch business is more concerned with cost optimization than mass optimization.

Atlas V offers two variants of Centaur, with one or two RL10 engines on it, although the two-engine version hasn't yet been flown on an Atlas V; adding solid rocket boosters seems to be incrementally more cost-effective than using the (very expensive) second engine.

Similarly, the Delta IV has two different second stage options with 4- and 5-meter diameters (DCSS-4 and DCSS-5); the tankage is significantly larger on the latter.

Angara uses two entirely different second stages.

That leaves Falcon Heavy; it wouldn't surprise me to eventually see a (further) stretched upper stage to take advantage of the more powerful booster, but in the near term, I assume that the cost optimization of using a common second stage outweighs the potential performance optimization, particularly since there's almost no market for single payloads that size.