Some points against a Nintendo Android based OS.
1. Games will not necessarily increase by simply having Android as the OS. Most Android software uses Google's closed source APIs and services and those will NOT be on Nintendo's OS. So in effect, games will have to be ported to Nintendo's platform anyway.
2. The reason why Google's services will NOT be on Nintendo's Android fork is that Google's services are all or nothing. Want anything from Google on Nintendo's OS, even services to make things easier to port? Nintendo better be prepared to allow the Google Play store on their hardware. Now Nintendo has to compete against Google on their own hardware.
3. Nintendo could follow Amazon and recreate all of the missing APIs and services so apps can be easily ported, but then that becomes a nightmare. First, they're basically writing chunks of their own OS anyway and secondly, Nintendo would have to keep up with any changes Google make to their APIs and their is no evidence Nintendo would be effective at this. Amazon certainly struggle.
4. Any games that Nintendo develop for mobile platforms would be tied in to Google Play services and wouldn't even be initially compatible with their own Android version. Any idea of sharing code between mobile and handheld/console would be difficult at best.
5. Software support has more to do with hardware strength and sales than it does with the OS support. Developers won't flock to Nintendo hardware just for running Android, especially when as mentioned they would either have to strip Google services out of their games or hope Nintendo has comparable APIs available and the sales won't be there compared to just dumping stuff on the Google Play store anyway. Developers aren't exactly throwing their games at Amazon's app store.
6. Open Handset Alliance members aren't allowed to build non-Google approved devices. Basically, a lot of manufacturers would not be allowed to supply hardware, whether that is a SoC or individual components. AMD isn't a member so this may not be the biggest issue, but get ready for higher hardware prices or lower hardware quality because of all the maneuvering that has to be done for non-OHA components that AMD can't supply. Renesas components on Nintendo Android based hardware? Not happening.
7. The platform can be locked down and made hard to root, but the possibility is always there. Unlike most Android devices, which are released for about a year and then retired, we are looking at three to five year life cycles and significant interest in the hardware. Both the Wii U and 3DS have been hacked within a couple of years of release with a handful of people, how long would it realistically take thousands of Android hackers to do the same?
I do apologise if I cover points that have been discussed to death, it took quite a while to type this out.