Wifi? there have been problems - and fixes. I assume that is the only thing that could take so long (though download an OS why should it take longer than downloading three full length movies from iTunes Store? it shouldn't)
Clean? just clone your system or make sure you have a good backup (or two) and with the actual install process - not the download which is separate issue - it can go like light-ning on an SSD in minutes. And Setup Assistant? nice good way to start off.
I would say there is no way to know if your system will run better or not or if it takes longer in the end, or just 'safer' and more stable method to get ML installed.
And you do want to save the installer so you can avoid downloading another 4GB later.
Free space or lack thereof is one factor, or maybe it is time for an SSD or new hard drive; swapping out the hard drive before it fails or checking to see if spare blocks have been used is best indication of likely or impending drive issue.
There are guides how best to put Lion/ML on 8GB USB and using Disk-Maker
http://blog.gete.net/lion-diskmaker-us/
https://www.macworld.com/article/1167857/how_to_make_a_bootable_mountain_lion_in stall_drive.html
Making sure your disk drive does not have any errors can only be done by spending time and effort and scanning for media errors or having a program that will - and a new OS is a good enough time for that.
Mac users just need to stay up to date and make sure your hard drive is free of errors,
Mac App Store, OS X Lion
When attempting to purchase or download OS X Lion from the Mac App Store wirelessly with your Apple ID account, you may receive a dialog stating "Your Device or computer could not be verified. Contact support for assistance." This could happen when upgrading Mac OS X v10.6.6, 10.6.7, or 10.6.8 to OS X Lion via a Wi-Fi connection.
Use the following steps to delete your network preferences.
Important: You must be logged in as an administrator.
- Click the Finder icon in the Dock.
- Choose Go to Folder from the Go menu.
- Type /Library/Preferences/SystemConfiguration
- Copy the file networkinterfaces.plist to the desktop (to make a precautionary backup).
- Delete the file "networkinterfaces.plist." from SystemConfiguration.
- Restart your Mac.
- Create new location in Network preferences, in System Preferences.
Once your computer has restarted, you will need to refresh your network settings to be able to connect to the Internet again:
- Choose System Preferences from the Apple menu.
- Choose Network from the View menu.
- From the Location pop-up menu, choose "New Location".
- Type a name for your location and click OK.
- Click the Apply Now at the bottom right to accept the changes.
If your network connection requires any special settings, you will need to enter them again.
Once you have made these changes, you should be able to connect to the Internet, open App Store, and try your OS X Lion purchase or download again.
This issue may occur if your Mac's Ethernet
port is damaged or inoperable, even if you aren't using Ethernet to try to download Lion.
https://support.apple.com/kb/TS3925