There is an event that can be triggered when dropping a native control onto an XPage or Custom Control. That event is used to enable the library in Xsp Properties. It's also used to enable the relevant abbreviation (xe, xc etc) on the pages. The bottom line is copy and paste isn't that sophisticated!
And it's not exclusive to the Extension Library. Try copying and pasting a Custom Control to a brand new XPage and save it. It will give you virtually the same message, but this time saying "xc" is not bound.
You need to enable the Extension Library manually if you're copying a custom control across. Alternatively, you can just drag and drop any Extension Library control onto any page in the application, then delete it!
If you're copying source code from one XPage to another, if it includes anything other than an xp tag, you need to check the relevant xml namespace is specified in the xp:view tag. So in the case of copying source code for the application layout, also adding xmlns:xe="http://www.ibm.com/xsp/coreex" to the xp:view tag.
(This was too long an elaboration to just add as a comment to Jesse's answer, which I've up-voted)