Why do we only add boosters to increase payload launch by a rocket?

I may be mistaken but it seems to me that to increase the payload a rocket can put into orbit, manufacturer add booster but do not modify upper stage(s).

• falcon heavy is a falcon 9 with additional booster strapped to the first stage
• ariane 6 variants differs only by the number of boosters
• the same happen with the delta IV variants.

To me it seems more logical to increase power of both the first stage (by adding boosters) and the upper stages. By only modifying the first stage, this stage may reach at greater acceleration, speed and altitude and thus operate in a non optimal flight environement (assuming the variant with less boosters operate at optimal acceleration, speed and altitude).

I'm not quite sure I'm understandable, so feel free to edit/suggest edit

• If it is possible to increase the payload by adding boosters to the first stage only, why should the upper stages be modified too? Keeping it as simple as possible and avoid modifications if possible. A redesign of all stages may save some fuel, but will cost a lot of money, much more than the cost of extra fuel. – Uwe Sep 9 '17 at 19:19
• Early on, increasing a rocket's payload capacity by using a more powerful upper stage was used quite often; for an example, see the sequence of Atlas D (no upper stage)Atlas-AbleAtlas-AgenaAtlas-Centaur. – Sean Jun 1 '19 at 22:46

Rocket manufacturers are optimizing for cost, not for total mass at launch.

It's cheaper and easier to modify one thing to improve overall performance, even if the result isn't mass-optimal, than to modify two things.

In the Delta IV medium, Atlas V, and Ariane 6 cases in particular, changing just the number of installed SRBs is both cheap and flexible; you can start building an inventory of launcher cores and SRBs well in advance of knowing what payloads you're launching! They don't have to design different boosters, different cores, or different upper stages, they just pick the right number of boosters to do the job. Manufacturing a bunch of modular boosters is cheaper than developing several different kinds.

That said, upper stages may also get small customizations for different configurations. Falcon Heavy may need some structural work on the upper stage for heavier payloads. Atlas V has a two-engine version of the Centaur upper stage (though that hasn't flown yet, and the single engine version is more mass-efficient). Ariane 5 refined the boosters, core, and the upper stage over various iterations.

• Increasing the number of SRBs is very simple, no extra development is needed. The SRBs are ready to use and the first stage too. Only more mountings points for the extra SRBs are added. Of course the structure of the first stage should have some stability reserves for the addition of boosters. – Uwe Sep 8 '17 at 21:15

Frankly, it's just plain easier and cheaper to slap on additional boosters to the lower stage than to add capability to the upper stage. Every Kg of mass you add to the upper stage translates into N Kg of additional propellant in the booster, and N can get impractically large in a hurry.

Also, where thrust (power) matters more for the booster, specific impulse (efficiency) matters more for the upper stage. You're better off using a lower-thrust, high-Isp engine on your upper stage than slapping more high-thrust, low-Isp engines to it.

Comparing the Falcon 9 and Atlas V vehicles:

Rocket    Mass to LEO    Mass to GEO
------    -----------    -----------
Falcon 9  22800          8300
Atlas V   18850          8900


F9 can lift more to LEO, but the Atlas can lift more to GEO. That's because the Atlas uses the hydrolox Centaur upper stage with the RL-10 engine, which has much lower thrust than the kerolox F9 upper stage with the MVac (99,100 N vs. 934,000 N, per Wikipedia) but a much higher specific impulse (451 s vs. 348 s, same source).

But, practical engineering considerations come into play. Hydrolox stages are expensive - because of the low density of LH2, the tanks have to be a lot bigger to hold the same mass of fuel, they have to be kept much colder, etc. The F9 is as wide as it can get (~3.6 m diameter) and still be road-transportable. They can't stretch either stage to be any longer because the whole stack is as tall as it can get for its width (otherwise it can bend due to wind shear). SpaceX chose to use common materials, tooling, and propellant for both stages to keep costs down.