Collision entropy definition
When $X$ is distributed uniformly over a domain of size $n$, then Shannon entropy, collision entropy and min-entropy are all equal to $\log n$. In a sense, all of these parameters measure the amount of uncertainty in $X$.

In contrast, your proposed definition is always between $0$ and $1$, tending to zero as $X$ gets more unpredictable. This is quite different from other notions of entropy, in which zero stands for predictable.