I have such nostalgia and cozy memories of this show and the books def serve that purpose for me again, but I absolutely recognize how our FMC Jessica Fletcher gets away with being a white women with privledges, a nosey lady without consequences. She is never innately cruel and definitely goes out of her way to be opening and welcoming as possible to everyone she meets, but the character still sits tight in her white patriarchy role without realizing her abuse of that power. 
She solves murders with a down-home-plucky-do-gooder curiosity in a meta-ish formulaic way and I appreciate that vibe.  Don't overthink it, but recognize it for what it does.

Fun theories are that Jessica  Fletcher is the serial killer and that Cabot Cove has the most murders per capita in the country.