Again, I'm looking for the "aha!" in the linux home desktop space where windows and os x fall down, but linux works or has something the others don't.
I'm not sure I want to claim that there is any slam-dunk feature where Linux smokes the competition.
But the Linux package management system is so much better than the Windows situation. The Windows model is: go to web page, download installer, run installer, trust that the installer is not doing anything bad. Note that these are the same steps whether you go to "SafeVettedKidsSoftware.com" or "MalwareToWreckYourComputer.com".
With Ubuntu, you can get the packages from an "app store" GUI application that pulls from the Ubuntu repositories. You can find a category (like "Games") and click around in the GUI, find something interesting, click, and it downloads. I don't care if you are an adult or a 7-year-old, that is just easier than Windows.
Windows wins on software availability. Almost all the software available on Linux is also available cross-platform, but the converse is definitely not true. But there is a ton of free cool stuff on Linux, and he is less likely to end up with malware installed and popping up porn ads.
I know a high-school boy who is has learned Linux; he wipes computers, installs Linux, installs additional packages... he doesn't use the "app store" GUI but rather uses the low-level tools. He has a better skill set than I had at his age (albeit he also had access to all this cool stuff and I didn't). I don't know if he will study computers when he goes to college, but if he does, he already knows a lot of the stuff that the intro classes will cover. Linux has been good for him.
The only problem with your thesis is that you presume there is a great chance of getting malware from non repository software.
Sorry, but I'm unlikely to get malware from Disney, Nickelodeon or the long time developers of Kidzui.
Plus my 7 year old appears to have mastered finding the software he wants, asking if he can install it, and doing so. So it seems to be not that complicated.
How many times have we gotten malware on our 7+ home computers? Never. Couple of times malwarebytes or security essentials complained about something, and on occasion they block access to a web site because its been reported to have malware. Zero infections, because we don't surf russian porn sites, we don't install shovelware, and we don't click OK on anything that pops up and says "Hi, can I install your free ?". Pretty straightforward.
Then there is the associated funny business with well established software, which mimics my linux OS installation experience. You always have to edit some files, find some obscure software, or use odd troubleshooting methods to make simple things that work just fine under windows work under linux.
To wit, here's the minecraft for linux download link description:
"The jar is executable and might work as-is. If you run into memory issues, try launching it with java -Xmx1024M -Xms512M -cp Minecraft.jar net.minecraft.LauncherFrame, also please use Sun's JVM."
MIGHT work as is. Or just use this obscure launch string to try to make it work. When that doesn't work, you can post a question on some forum, where 20 eleven year olds will taunt you to read the 400 page wiki, search the last 3 years of threads, and then declare you a dumbass because you can't figure it out on your own. Oh, and someone want to clue me in as to how my 7 year old will determine if he's having a memory issue or not?
Wizard 101 (the other hot elementary school kids game) has two pages of instructions on how to install on linux, including installing Wine and tweaking stuff. On the flip side, the 8 year old from across the street installed it on one of our windows machine, with a few helpful tips from my 7 year old. While my wife and I were watching tv undisturbed.
Then we're back to the original point of "Why do this when the computer already comes with windows, windows works fine, everybody knows it, they use it at school, and we've already determined that there is no killer app or capability that linux has that windows doesn't"?
Answer: People are fond of it for various reasons, but there isn't any good reason to foist this on a young child. You're going to give them something unfamiliar, complicated, and they won't derive any benefit from using it. About the only outcome of that is to make the child more dependent on you to resolve their issues, and when you have kids, you'll find that what you want is the opposite of that. You want to enable them to figure things out on their own.
Oh, and whoever keeps modding me 'troll' on this, grow up. Your little tech toy operating system isn't appropriate for small children or most other people for that matter. Get over it. At best you're limiting their worthwhile development scope by foisting this on them. At worst, you're teaching them stuff they'll have no use for, while skipping a prime opportunity for them to develop skills they can use on the computers at school.
To wit: my kid helps me start up all 30-something computers in the school lab, helps other kids log in, run the browser and get into their apps. He can do this because he's been given experience in the platform that ~95-something% of schools use. His peer students think he's a superhero. If he used linux at home? He'd have almost zero applicable skills to help his fellow students.
Once again, to get people to adopt something, you need a compelling story and capability set that is so much better or only available on a platform that it overwhelms the cost and hassles of adoption. That isnt and has never been the case with linux. Its a solution in search of a problem.