The aesthetic appreciation of Da Vinci's work would make it a cultural icon.  The portrait is a study in painting technique with its technique in both subject display, texture, foreground, and background, as well as symmetrical designs.  It is something that has come to be appreciated as a landmark art work.  I think that its vaulted viewing position at the Louvre has also helped to contribute to its cultural icon status.  People go to the Louvre, in large part, to see the Mona Lisa.   This is only enhanced by its staging in bulletproof glass, impermeable to the elements that could wither paintings like it, and to ensure that individuals who view it recognize that they are standing in the presence of something iconic.  At the same time, the wealth that the painting could generate on the open market continues to add to its iconic status.  I also think that the fact that so many artists have referenced or parodied it do help to feed the idea of a status that represents iconic.  Warhol's pop culture interpretation of Da Vinci's work is only an example of this.  I think that one can get the full effect of Da Vinci's work's iconic stature by surveying the internet to see what a search of the work results.  The images seen are both representative of the legacy of the painting and how it has become iconic in so many different ways.