MacBook – the ribbon in this picture of a 2006 MacBook

You're not the first person to have problems with this drive in a Mac - see http://www.mac-forums.com/forums/apple-notebooks/217444-macbook-pro-hard-drive-replacement-wont-format.html

It's possible there is a compatibility issue, as you seem to be doing all the right things (and it is connected properly otherwise you wouldn't see it in Disk Utility at all).

The damaged hard drive bracket would not be the cause of the error above.

Try a non-AV drive (one designed for notebooks rather then surveillance/home theatre use) and see if that makes a difference.

Recycle or sell it for parts. Since the GPU is soldered, you likely cannot bypass the temperature sensors that the system monitors to ensure safe operation with consumer skills at soldering. Have you looked into a logic board repair or buying a Mac with a shattered screen at low cost to assemble one workable Mac?

Operating a machine where you know the protection mechanisms are shutting it down to prevent overheating and persist in doing so, being frugal crosses a line into taking risks with fire if you don't go to great lengths to protect yourself and other property nearby.

Also - your characterization of design flaws seems unsupported with one link to a 540 entry discussion thread. A six year old computer having failures seems more like a car needing an engine rebuild after things start failing and not so much a design failure, but perhaps the link wasn't correct.