Support

No, this will not be possible. Have you read the thinking behind it? The core Joomla! Update component shipped with Joomla! 2.5 and later is written and maintained by yours truly. It's the same code as Admin Tools' former Joomla! Update feature. The problem is that the Joomla! project changed the way they are handling pre-release versions making it impossible for Admin Tools to determine if an available Joomla! package is an officially released update or a pre-released testing package. As a result we'd have to use the XML update file to find updates (the same one the Joomla! Update core component uses) instead of getting this information directly from JoomlaCode.org (where all Joomla! releases are listed). This meant that the following features could no longer work:

• Re-install your current Joomla! version (we no longer have a list of old packages)
• Present the current LTS and STS releases and let you choose which one you want (they are listed in different XML update files)

That made Admin Tools' feature functionally equivalent with the core Joomla! Update component. I am the author of both. It would be a profound case of mental masturbation having to maintain two different code bases achieving the exact same thing in the exact same way with the only difference being the interface.

If you want to reinstall your current Joomla! version, of course you can. You always could, ever since Joomla! 1.6. Admin Tools didn't make it possible, it made it obvious. The non-obvious Joomla! approach (one of the two, I'm presenting the one which doesn't involve downloading/uploading anything):

1. Go to http://www.joomla.org/download.html
2. Click on the "Upgrade Packages" button (Joomla! 3.x) or the "Other Joomla! 2.5.x packages" (Joomla! 2.5)
3. You will see a Joomla_X.Y.Z-Stable-Update_Package.zip file, where X.Y.Z is the latest Joomla! version. Tip: if you need an older version, from the left sidebar click on the Joomla! version you want (e.g. 3.1.0), Browse Releases and find the package you want.
4. Right click on the package you found and choose Copy Link Location (or whatever your browser calls it)
5. Go to your site's Extensions, Install / Uninstall
6. In the Install from URL area paste the link you just copied and click on Install

Admin Tools did the same thing behind the scenes, with the only difference that it didn't use the Extensions Installer to extract the package. If you have trouble with this method, substitute the following steps (steps 1-3 are common):

4. Download the package ZIP file
5. Upload it to your site's root
6. Upload Kickstart on your site
7. Run Kickstart
8. At the end, click on Run the Installer
9. Close the installer tab
10. Back in Kickstart's tab, click on the Clean Up button

You're welcome, Arno! It's not an advertised feature and should only be used in case of an emergency (e.g. when a client "accidentally" deletes core files), but there you are, it's perfectly possible :)

For completeness' sake, something like that was also possible with Joomla! 1.0 and 1.5, as long as you'd follow the Kickstart method (there was no provision to install Joomla! through the extensions installer).