Why doesn't aromatic substitution add at multiple positions in one reaction?
The rate of Aromatic substitution depends upon the activity of the aromatic system, because when the collision happens the aromatic system has to donate electrons to an electrophile.
In the example above you have used nitro-benzene, which is very strongly deactivated due to the $\ce{-NO2}$ group and thus the ortho and para positions are completely blocked. The meta position of nitro-benzene is not good but also isn't as bad as the para and ortho positions, in terms of electron density. So, we can say that the meta position of nitro-benzene is just a smidgen less electron rich than normal benzene, and thus first bromination takes place. But, after the addition of one bromine the ring becomes even more electron deficient which just makes further bromination even harder and slower. The reaction slows down to such an extent that it practically ceases to proceed.
On the contrary, if you would use a strongly activated aromatic system like phenol or aniline. It would provide such electron density to the para and ortho positions that they would undergo complete bromination, forming a 2,4,6-tribromo product. The electron density provided by $\ce{-OH}$ and $\ce{-NH2}$ is simply so high that it overcomes the electron deficiency created by the added bromines.