The 810 has been called the "flagship" of the Taylor lineup but I tend to agree that a GA with a cutaway is probably the stereotypical Taylor that people think of.
That being said, I'd submit that there is no truly "iconic" Taylor guitar. And that might not be a bad thing. Three reasons why:
1. Taylor doesn't have near the amount of history and legend as brands like Martin, Gibson, or Fender.
2. This means they're not bound as much by that history and instead have made innovation their hallmark rather than tradition. They have more freedom to change up appointments and features without being accused of sacrilege.
3. Taylors are relatively consistent across the range of shape and series in terms of having the Taylor overall look and sound -- that has changed a little recently with the 700 and 500 series models.
I actually think the "icon" of Taylor Guitars isn't a specific model, but rather Bob Taylor and his approach to building guitars. That is the legacy that people have tried to imitate and that is what history will remember. And I think that's pretty awesome.