"I don't think I'm alone when I plan to have a backup flashlight/headlamp. Even the best piece of electronic equipment on this planet can, and does, fail. I can't think of a prudent reason not to have a back up…I hike alone and wish to minimize risk."
The way I see it, when you are day-hiking the sun is your primary source of lighting. Carrying one flashlight is carrying a backup light source because you never intend to use it. This is different from overnight hiking where at times you may be relying on your headlamp/flashlight as your primarily light, and thus you may want a second light as back up. Even then, I consider a second light more of a luxury. If the first light were to fail and I didn't have a second light it wouldn't be a big deal. A few years ago I was on a 5 day hike and on the third day my only headlamp was turned on by an impact to my pack and when I reached camp that night I found it was dead. It kinda sucked, but it wasn't a real problem in the life or death sense.
The only reason not having light might be a big deal is if other problems are occurring at the same time, like not having enough warm clothes to survive the night, so you need to get out immediately before hypothermia sets in. This is a troubling scenario, but the real problem is not the lack of lighting, but rather it's the lack of insulation. If you have the true essentials covered, then your light failing won't be a life or death problem.
Based on your concern about risk, I presume on your day hikes you are already carrying a basic shelter (ie. tarp or emergency blanket) and enough warm clothes to get you through the night. If you did get lost out there, would you really try to hike out at night? I would most likely stay put for at least the night and use my shelter and warm clothes. I guess my point is that even in a scenario where you are lost, a flashlight is more of a luxury item compared to essentials like shelter and insulation. On survival shows (ie. Survivorman) I don't think he ever has a flashlight/headlamp. You're right that a light could fail, but if you are properly prepared in all aspects then this shouldn't pose a serious risk.
If you are not carrying enough warm clothes or a shelter and are relying on a hiking out at night, then yeah I would want a second light. But a better approach would be to not rely on hiking out at night.
As a final comment, those tiny Photon lights do provide enough light to hike with in an emergency and they are super reliable because they are so simple. These are what I use for a backup light source. Even if it was to fail, I could probably pop it open and manually connect the LED to the battery using two wires to get light. If you want to spend more money on a more respected brand, Princeton Tec makes something similar called the Pulsar.