I would say All-American Girl is the "most famous" song from the era, since it seems to be one of those songs you hear mentioned along with Carrie's name all the time, aside from the obvious ones like BHC and JTTW.
In my opinion, Carrie's signature songs are BHC and JTTW (tied for first place), and then AAG and "Undo It" would be 3rd and 4th.
I think you are correct about AAG being the "MOST famous" song from CR. I am interested in what you think are Carrie's signature songs. I completely agree with BHC and JTTW and I really think agreement on those two songs should be universal but then for me it turns into different perceptions or perspectives and that is VERY interesting. I feel like I live in the micro-world of Carrie sometimes so I don't know what someone would say who isn't a "super-fan".
I think if one expands out from BHC and JTTW, what songs are really Carrie signature songs or are there any?
I would say recently b/c of Carrie's EXTRAORDINARY GNO performance of HGTA she has temporarily co-opted that song (Along with her singing it in concert "in concert" with JTTW). Obviously it has been sung by many people over many years. I know Elvis used to perform it at his concerts. I just think that right now, if I were another singer I wouldn't choose to sing it b/c Carrie is currently linked with the song in such a positive way. I feel like I am not expressing this well and again I may be clouded by my great exposure to Carrie and lesser exposure to other artists.
I think AAG probably is the most signature song from CR. I was surprised to see you mention Undo It. I don't know if anything from Play On reached the level of signature song.
Anyway, thank you for your comments. They made me think and I enjoy reading others' opinions and views.