Why don't halogens form cations like H+?

The first ionization energy of hydrogen is $1312\;\mathrm{kJ\cdot mol}^{-1}$, which is larger than that of halogens such as chlorine, bromine, and iodine.


Given that observation, why don't halogens form $\ce{X+}$ ions like $\ce{H+}$?


