I know.
I live in a suburb of Memphis now, and I first heard about this story on one of the national news channels. There's no place in or around Memphis that's "safe" for a petite woman (or anyone) to be jogging alone anytime, certainly not at 4:30 a.m. Memphis is odd in that you can be driving through a very upscale neighborhood with manicured lawns and TREES, lots and lots of trees here. It's like living in a forest. One block up the road you're literally in the 'hood. Not the worst 'hood (I took a wrong turn a couple of times and was faced with the REAL 'hood, and I couldn't get the heck out of there fast enough!), but not great. The houses are unkept, and there are no trees. It's as if the trees "know" something. Then a few more blocks, and you're in a neighborhood of 100-year-old mansions owned by doctors and lawyers.
I've lived here since 2006. My parents were both from a small town in NE Arkansas (the one where no one locked their doors) and moved to Houston, TX before I was born, so I lived in Houston the first <ahem> "several" decades of my life, so while I've never lived in fear, I've always done what I could to best insure my safety. It's just what you do when you live in a city. One night my mom was going to some evening function at the church when she was stopped at a red light. Fortunately she was the first car. While waiting, she said some man... laughing like a maniac... pulled one of the back doors open and tried to get in. She just gunned the car through the red light and left him rolling on the street. That maniacal laugh stuck with her. As did ALWAYS immediately locking all the car doors as soon as she got in. To this day if I'm in a parking lot my head's on a swivel. I've got my key fob in my hand, and the second I get inside I pop all the door locks before doing anything else.
The night after Eliza Fletcher's body was found, a conservative news show host I listen to regularly talked about the case in his opening monologue. He was appalled that he saw a lot of people on SM expressing things like, "What did she expect jogging alone there at 4:30 in the morning"? (She was in the University of Memphis area which, at least after dark, is a known drug/thug hangout.) He thought the implication people were making was she "asked for it." No, she didn't. No one deserves what happened to her. But, as you said, she could have run on a treadmill in the safety of her home, and there are indoor running tracks many places which she could have made use of. I can understand her husband, who has a job, didn't want to go jogging at 4 a.m. Besides, someone needed to be at home with their children. I'm not big on husbands who want to control their wives, but in this unusual case I really wish he could have put his foot down and then helped her with alternative ways to get her miles in.
My mother, ordinarily a quiet, polite, genteel Southern lady, had some pretty progressive ideas. She thought (and I agree) the death penalty was too quick and painless for POSs like this one, especially considering it takes many years of exhaustive appeals before the sentence is actually carried out. She proposed either an immediate trip to the "chopping block" where his manhood would be permanently separated from his body, and he would probably exsanguinate pretty quickly. It'd just not be as comfortable and easy as an intravenous cocktail. Or else hanging. Not by the neck though because most of the time that results in a quick death, too. Rather she proposed hanging POSs like this by their "manhood," the step kicked out from underneath him, and just let him hang there until his "parts" rot off. If you had known my mother you would have probably been surprised to hear her thoughts on this subject, but she had some interesting ideas.
Rape anyone, SA a child or non-consenting adult. If these people knew they're going to have to part from their "favorite" parts, I think you'd see a marked decrease in sex crimes. It's like back in the 1800s when they'd have gallows on the town square. Convicted criminals would be strung up, the trapdoor would open, and "zing!" I imagine that was pretty good deterrent to violent crime.