Frank, let's compromise.

When dealt AQ offsuit and three low cards you can hit a royal holding either the Ace alone, or the Queen alone, or drawing 5 new cards. You will never draw a royal holding AQ offsuit.

When playing Bonus poker you will win more money holding AQ than trying for a royal holding either the A or the Q or drawing five new cards.

But, let me throw a little twist to the problem: when playing Double Double Bonus or Triple Double Bonus, the correct play is only to hold the Ace when dealt AQ offsuit.