The Falcon did fire missiles actually, at The Death Star's reactor.
Always thought those were just blaster fire. /shrug
Doesn't really matter, doesn't effect my point other than it brings up Hans incompetence for not using them on Ties before that point.
If Han had used missiles on the TIEs in the trench in ANH they would have been alerted to his presence that much faster as they would have been alerted to the target lock. Not to mention, Han is playing to the Falcon's strengths, which is certainly not tailing a much smaller and more maneuverable adversary.
Doesn't explain why he doesn't use them during the Death Star escape, the Hoth escape, the battle of Endor prior to the reactor you know, any time he ran into Ties
So, what, you think a smuggler just carries a munitions payload everywhere he goes in a galaxy where those could be immediately detected by passing Imperial patrols, drawing further attention to himself..?