The way Apple chose to implement changing iCloud-account is far from making any sense at all. The phrase "Delete Account" puts every users' imagination into high gear. By clicking this red button what could possibly go wrong! Does it implode your entire iCloud-account with all the data in it so that everything is gone permanently and forever? Or does it simply disconnect that particular iOS device from the Apple's cloud?
To actually change the device to use a new iCloud account is much more tricky, as the article points out. And on top of that, iMessage, Facetime and AppStore still need to re-connect separately. Luckily that's not a big deal at that point.
However, if you combine changing the account with taking a new iPad into use, then you see a flood of e-mail from Apple. The e-mails come from different systems at Apple, but it certainly made me laugh a for a while. There are e-mails from Find My iPhone (my device was iPad), then there are security notifications about Apple ID being used in a new device and when all is set up, there is the welcome to a new device -mail. It would sound like a better idea to switch the account into some sort of changing-devices -mode, but they don't have that yet.
The good thing is that it is possible to change accounts. The bad thing is that they implemented the bare minimum of it.