How to flush apps from iPad2 using a "Restore from backup"

Question

When I receive an iPad back from loan (library environment) it frequently has additional apps loaded by the borrower, over and above the small set of apps that we provide when the iPad is checked out.
If we reset the iPad (Settings/General/Reset/Erase All Content and Settings) and then restore from a canonical backup, the iPad is rendered "fresh" with no evidence of the previous borrower and ONLY the small set of apps that we provide.
However,
If we simply restore from the canonical backup, without the reset, the evidence of previous use is limited to just the additional apps that the previous borrower installed. In effect, the iPad contains the union of our standard set and the previous borrower's additions. All the data, media and settings (even defaults such as iCloud and Store IDs) are removed. The iPad is "fresh" except for the additional app or apps.
The simple restore from backup is much faster than the reset+restore and would be preferred.
Manual inspection and removal of borrower-installed apps is too time consuming.
Looking for a procedure that would force the app list down to only the one in the backup...
Any comments?

Answer 1

=> ex_spy_guy
Thank you for your prompt and thoughtful comment.
The library is institutional but is not publicly funded. Our policies are not traditional, therefore.
We wished to give the early patrons the ability to experiment with apps of their own discovery that they provision using credentials that they already have or that they create for the purpose. We have no record of their credentials and they do not have the Library's credentials. We never attempt nor allow the iPads to be sync'd on our duplication station. I agree with almost everything that you are saying but:
- we loan a "fresh" iPad that has been restored from a tightly controlled (never sync'd) backup
- we are returned an iPad that contains the initial app set + user settings, media, bookmarks, history etc. + one or more apps that the user has installed using his own credentials
- the iPad is connected to iTunes (on Lion) with automatic sync disabled
- we control-click on the iPad device name and restore from backup using the virgin backup mentioned above
- the restore takes 10 seconds or less since no new apps nor media is added
- the resulting iPad contains no user settings nor data but does still contain the app(s) that the user added
- if the iPad is reset to remove ALL non-firmware apps and then is restored from the same image, the users apps do not appear, just as one would expect. This takes 10-12 minutes with the app set that we currently provide. We find this burdensome for frequent use but it's perhaps necessary...
It surprises me that the users' apps survive a "Restore from Backup" process.
Unlike a traditional disk image (OS X .dmg for example) the iPad restoral "image" (~Library/Application Support/MobileSync/Backup/) contains no binaries. It's just a manifest of XML files in a folder and describes what .ipa binaries should be loaded from the iTunes library. iTunes does not, apparently, exclude (delete the encryption key of) binaries that are not provisioned in the manifest. Everything else gets zeroed-out of the iPads but not the foreign .ipa files. Is this a feature or a bug?