Android is the most popular because it's the perfect choice for most manufacturers, carriers and users as well. It's open source and fully customizable, this benefits all the three parties I mentioned. Manufacturers can personalize the OS completely and give it their personal stamp to make it different to other phones, carriers can also make some changes and add their own apps in order to differentiate as well, and the users can also customize it and they can also bring unofficial updates to phones that aren't updated by their manufacturers. Another strong point is the apps, it has all the apps and games a user could want and most of them are free, with the option to pay for additional features or removing ads. The OS is available in all kinds of devices: Smartphones, tablets, cameras, music players, etc. at every price point, which makes it the most accessible platform. iOS doesn't have this and Windows Phone is only recently starting to follow this strategy.
I personally think Android is a good OS, it's not perfect and it has the popular issues like lack of updates from manufacturers, deficient performance in low-end devices and to a lesser extent it also has malware and viruses, but in general it's good and has improved a lot during the last 2 years. If you have Android 4.0 or higher, you can notice that it's a solid OS. It's the most popular mobile OS because even if it's not the best, it has the key point: ACCESSIBILITY. iOS is not accessible at all, it's only designed for high-end purposes, and Windows Phone followed the same route as iOS until recently. I personally think people should give it a break, it gets a lot of hate but it truly is a good OS, I can understand the criticism for low-end devices and have experienced it myself, but it's wonderful in high-end devices like Nexus, Galaxy, etc.
I've gotta say, I disagree with almost all of your points. First I should preface this by saying that I have thoroughly used android on many different devices and I have many issues with it. I will start off by saying that the nicest thing about android is that you can do the most with it: Since you can root it and the end user can modify it how they see fit, the most can be done with it. Now how you say that Windows Phone and especially iOS aren't accessible is beyond me.
First you start of saying that manufactures and carrier personalizing the OS is a good thing, and I highly disagree. I have only ever seen one instance where a manufacture had skinned android (sense 1.0-2.0) and it was better than stock android. Other than that, I think all of the other skins, for lack of a better word, are garbage. I mean, take touchwiz for example: I played with the new samsung galaxy note 8.0 recently. I noticed that once in a while it would lag, thats unacceptable for a brand new device running a fairly powerful quad-core exynos processor. Also, I though it was without a doubt the most hacked together user experience I've ever seen: There were 2 app launcher bars, seriously, one on the side and one on the bottom, also, when you hit the buttons on the bottom of the device, it does different things like if you double tap the back button, vs hitting it once, vs holding it down, essentially there were 9 different things you could do from the bottom tablet buttons...Kinda confusing to me. The point I'm trying to make is its the same deal with windows. I have never used a windows computer where I thought any OEM actually added value to the product, I feel whenever they load software, its crap trial versions of products that just get in the way. Thats why every time I buy a windows PC, I re install a fresh version of the OS so I don't have to have a norton window popping up every 5 seconds to remind me that I need to renew my subscription. If I were to every buy another android device, I would only get a nexus as I think stock android is far simpler, faster, and more intuitive than any skin placed on top of it.
You are right that android has come a long way, and I didn't think android got good, until 4.0, but I still feel it has a very long way to go to get to the same usability as iOS. My experience with android is that apps crashed frequently and even the OS itself crashed a couple of time on me. In the 2 years that I've owned my windows phone, only 1 app has crashed on me a couple of times (spotify for WP7) and the OS has literally NEVER crashed on me, ever. Same with iOS, I can only recall, maybe one time seeing iOS actually crash.
Now to the accessibility: How is iphone/ipad not accessible? If you're talking about price then I can understand what you're saying in terms of that iOS devices are premium products sold at a premium price, but the OS is dead simple to use, I mean it has one button! iOS is far simpler to use compared to android and is a little simpler to use compare to WP. In any case, both are much more fluid and fast than android is. iOS almost never lags, except for older devices, and I've never had wp lag. As for windows 8: It depends on the hardware..although even the atoms give a pretty smooth user experience.
Also, with regards to the free app comment: Yes android has many more free apps than WP and iOS, but that means developers also never make the same amount of money. Thats why all developers release for the iphone/ipad first. Yes, you can jailbreak an iphone, and its easy to do, same with rooting an android phone, but if you look at the numbers, people pirate more on android because its easier to do because its open. Yes iOS does have an issue with piracy, but more importantly, its a statistical fact that if you release an app on iOS, it will make more money than android (just google it). Also, its much easier to develop on iOS and WP than android simply because of standardized hardware. Every generation of wp use the same processors/gpus and theres only one current iphone and ipad out at a time vs android.
I'm not saying android is a bad system, but it does have a ton of issues that other OSes simply don't.