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

When  alcohol is treated with KI in presence of sulfuric acid the reaction occurs as follows :

STEP 1:

Thus the KI produces HI.

STEP 2:  Now the alcohol has to react with HI to produce alkyl iodide but sulfuric acid being an oxidizing agent oxidizes HI to produce  as follows :

Thus the reaction between HI and alcohol could not occur.

thus alcohol is treated with KI presence of non oxidizing acids such as phosphoric acid 

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