Indirect titration with ascorbic acid

We were doing a titration experiment to find out how much ascorbic acid a vitamin pill actually contains. In a flask, there is a solution of **water**, **sulfuric acid**, **potassium iodide** and **ascorbic acid**. Also starch as an indicator. When adding **potassium iodate** $(\text{KIO}\_3)$, the following reactions will appear:


$$\text{IO}\_3^- + 5 \ \text{I}^- + 6 \ \text{H}^+ \longrightarrow 3 \ \text{I}\_2 + 3 \ \text{H}\_2\text{O}$$


After the iodine is formed, the following reaction will appear:


$$\text{C}\_6\text{H}\_8\text{O}\_6 + \ \text{I}\_2 \longrightarrow \text{C}\_6\text{H}\_6\text{O}\_6 + 2\ \text{H}^+ + 2 \ \text{I}^-$$


After using the right amount of potassium iodate, there will be no ascorbic acid anymore, causing to eliminate the second reaction. When there is no ascorbic acid, iodine will not react back to iodine-ions, which causes the starch to give a brown/blue color.


My question is, why isn't this possible without the sulfuric acid? 


