Why is sulphuric acid not used during the reaction of alcohols with $KI$?

(N/A) In the presence of sulphuric acid $(H_2SO_4)$,$KI$ produces $HI$.
$2 KI + H_2SO_4 \longrightarrow 2 KHSO_4 + 2 HI$
Since $H_2SO_4$ is a strong oxidizing agent,it oxidizes the $HI$ produced in the reaction to $I_2$.
$2 HI + H_2SO_4 \longrightarrow I_2 + SO_2 + 2 H_2O$
As a result,the $HI$ required for the conversion of alcohol to alkyl iodide is consumed,and the reaction cannot proceed.
Therefore,sulphuric acid is not used; instead,a non-oxidizing acid such as phosphoric acid $(H_3PO_4)$ is used.