Why did they ‘split’ this H2+ ion in the ionic equation?
$\ce{H2+ (aq)}$ ions don’t exist. Furthermore, even if they did, they would not make a neutral compound $\ce{H2SO4}$ with the sulfate ion, since the sulfate ion has a $2-$ charge.

So you must split $\ce{H2SO4(aq)}$ into $\ce{2 H+}$ and $\ce{SO4^2-}$ ions.