“While the idea of being the last person on Earth may be fascinating for some, it could lead to some obvious challenges with regard to plot. The story would mostly be a fairly uneventful narrative.”
I'd like to reword that last sentence to read, 'The story might be a fairly uneventful narrative in terms of interaction with other characters (obviously).' However, that's not to imply that the narrative would actually be boring. It could be still be an intensely interesting story, incorporating interaction with wildlife, environmental obstacles, and even personal challenges such as coping with periods of total silence, loneliness, and attempting to keep one's sanity intact.
If you were the author, would you have your character become the very last person on Earth, and write about how they cope with that? Alternatively, would you have them find a mate, either early on in the story or towards the end, with the possibility of starting a new world all over again?
If your character really was the last person on Earth, would they know it or would they be 'left in the dark' about that so to speak? Not knowing would raise the tension somewhat, especially every time they entered a town or city. Would you have them enjoy positive experiences as well, such as driving a new car around the streets or a famous racetrack, befriending a pet, finding a treasure trove of canned food and bottled water, pumping their favorite music through some outdoor speakers, taking a boat for a spin or even flying a plane? Or would it be rather bleak, similar perhaps to The Road by Cormac McCarthy? What would you like to do if you were the last person on Earth?