This probably has to do with optimizing the launch efficiency of the rocket.
More specifically, a rocket has two goals:
- Get out of the atmosphere
- Reach orbital velocity
The second step can't really be accomplished before the rocket has "left" the atmosphere, because drag against the atmosphere doesn't increase linearly with speed: it increases with the square or even a higher power, once supersonic regimes are considered. This means that an "optimal" rocket launch is rather slow at the beginning, while the rocket is still in the thicker parts of the atmosphere, and then power is increased once the air is thinner and drag plays less of a role.
At the ~3km in altitude where the additional set of solid rocket boosters are lit, the atmosphere is already only about 70% as thick as it was at sea level, which means that the rocket is "allowed" to go faster without losing enormous amounts of energy to drag. If all boosters were lit directly on the launch pad, the rocket would presumably go too fast too quickly and thus waste a lot of energy. By spreading around these ignitions, a higher mass-efficiency is reached and more payload can be transported to orbit.