From what I remember, she wasn't particularly popular immediately before her death; however she was constantly in the press, so difficult to avoid (and fascinating, regardless of whether she was liked or not).
I don't think either Dodi or Diana were particularly invested in the relationship - I think it's more likely that Mohammed AF was using both Dodi (who was already in a relationship with another woman) and Diana (who was craving glamour and publicity and up for a freebie holiday) to further his own agenda (whatever that was).
So he dangles his playboy son in front of her, with tragic results.
As far as I remember, it was Blair who styled Diana "The People's Princess" in that interview following her death, and she styled herself Queen of Hearts during the interview with Bashir.
The Queen had to practically be dragged from Balmoral to make that announcement to the nation following Diana's death, and was subject to some pretty strong persuasion by Blair (who judged the mood right - that speech was probably the making of him).
Who knows what the Queen was up to and why did she act as she did? To protect the kids, perhaps, or because, by then, Diana was no longer a member of the family as such and considered an irrelevance by The Firm?
Had she lived, I doubt if she could have tolerated being a royal has -been. She would have moved somewhere where she was revered - America perhaps. She may have continued with her charitable causes and become some kind of ambassador for unpopular causes but she would have wanted to remain in the public eye. I don't think she would have approved of Kate but may have approved of Meghan as they seem to be more similar in personality.
Either way, she'd have wanted to be the top dog and may have struggled with her inevitable diminishing status.
She would have remarried I think - she was in her prime when she died after all, and still of childbearing age - but to someone wealthy with status and position but not someone with a serious and important job (ie not a Hasnat Khan type).
I think she would eventually have become to be viewed as something of an irrelevance. I think Charles would have married Camilla and Diana would have been pushed further and further out of the public eye because of that. I think she would have tried to assert and restyle herself as mother to the eventual heir to the throne ( a bit like the Queen Mother styled herself when George V1 died).
I don't think she IS regarded as a saint, actually - she was a polarising figure when alive and continues to be so now she's dead.
Interesting thread!