Validity of the leveling effect of water in nitration reactions
What you have gone wrong in this question is you completely disregard the fact that mentioned stronger acids than water are all in aqueous medium, in other words, dissolved in water. Thus, fast acid-base reaction ($\ce{H2O}$ acts as a base here) happens to give $\ce{H3O+}$ as the only acid in these mixtures (leveling effect of water).

On the other hand, concentration of sulfuric acid is $\approx 98\% (w/w)$. That means, approximately only $\pu{2 g}$ of $\ce{H2O}$ in $\pu{100 g}$ of concentrated solution. Therefore, mole ratio of $\ce{H2O : H2SO4}$ would be about $0.1 : 1$. Thus, ($\ce{H2SO4}$ is not leveling with water. That extra remaining $\ce{H2SO4}$ can be acted on $\ce{HNO3}$ in nitrating mixture as shown in your scheme (vide supra).

Note: As a rule of thumb, you may simply consider $1:1$ mole ratio of water and any stronger acid than water would be the limiting level for the leveling effect.