Security is a big reason. They stop updating older version of iOS once the new one is out. So they don't want customers putting old software on their devices which may have some terrible security holes and put their data at risk. And Apple doesn't want to waste resources maintaining old versions of iOS and issuing patches for security bugs.
I will start by saying, this is not meant to be an attack, just a counter point. I will have to disagree with this part. If this was true, they would shut down access to the app store, or anything else that would risk apple/users devices on older devices. I have an iphone 4 with cellular service that I use as a gps on my motorcycle. I readily buy apps, and have access to everything except OS updates. It requires very little resources to allow users of iphone 4's to jump back an OS, they only have to maintain the latest version of every OS on their server for download (or, not even host it anymore) but allow users to install it on their devices. If I had the ipsw file & had the ability to do the install myself, it would cost them 0 resources to install it BUT apple prevents it. If appointments show up in the Genius bar, all their response has to be is "For services, you must update to the latest OS, we no longer support this OS". Done...
But by forcing devices to stay on the latest OS installed, they are showing that they want users to stay on a slower OS, so the response can be "well, this device is old, you should upgrade the device"
For example, if you have a computer that originally came with Windows XP but you upgraded to windows 7, the average user would be incapable of going back to windows XP BUT, it is physically possible. You would have to have a full version of Windows XP (which you no longer can buy) and the knowledge of how to reformat the hard disk in a Windows XP format. You would then be able to get all the patches MS created up until the end of support.
By automatically downloading the latest iOS, or keeping the flag showing an update is there, they force users to new OS', and the average user has no understanding that they can go back, or even how to. I'm sure Genus' are told to never instruct users how to go back, or help them do so. Needless to say, they would have no idea that there is a time limit to being able to going back. Which then forces them to buy a newer device because theirs is slow now. Even though it isn't that the devices is damaged, it is the OS is not good for the device.