In studying the chemistry and qualitative analysis of anions, why wouldn't HCl be a good acid to use to determine the solubility of a silver precipitate in acid solution?

Answer 1

Because AgCl forms a complex ion with AgCl which makes it more soluble in acid HCl solution than it would be in neutral solution.
AgCl + HCl ==> AgCl2^-
There also are other complexes. (AgCl3^-2).