Question

Why are hydrogen ions NEVER found in an aqueous solution?

Answer 1

They are actually found in aqueous solutions, though they are not always written down because they form naturally. In reactions in acidic and basic equations, they are written down. The presence of hydrogen ions are actually measured by pH.
They are found with hydronium ion = H3O+

Answer 2

I think the proper answer is that the H^+ adds to a water molecule to form the hydronium, H3O^+ ion. Thus H3O^+ ions are found but not bare H^+.