In Lucas test $\ce{HCl}$ is used for acid-base reaction between $\ce{Zn(OH)Cl}$ to give $\ce{ZnCl2}$ and $\ce{H2O}$ which is kind of good because $\ce{ZnCl2}$ is formed again and used in first step quickening the reaction. But why don't Lucas test use other acids like $\ce{H2SO4}$ (and add $\ce{ZnCl2}$ in bulk) or $\ce{HClO4}$ (stronger acid than $\ce{HCl}$ may faster the reaction). But why $\ce{HCl}$?

Is it had to do with acidic strength of $\ce{ZnCl2}$ and acid (I mean if stronger acid than $\ce{ZnCl2}$ may react with alcohol)?