This discussion took a turn to nowhere fast.
The model number is likely rare online because just as soon as the iPad 3 came out, it was replaced by the iPad 4. The 3rd generation iPad was the one of the shortest Apple product lifespans at only 7 months.
The iPad 4 is basically an iPad 3 with a new chip, new front camera, and new Lightning connector. There are few results for the iPad 3 online because the iPad 2 has been around since launch, and the iPad 4 took over the iPad 3's spot in the lineup. Not many were around because of the sheer limited availability.
That doesn't make it any less of a device, though. I just bought one for a relative, and I'm now on the hunt for one myself. It's price and features are ideal to someone who doesn't need the latest and greatest. For example, I have no Lightning cables or accessories, and no need to spend a premium to lose my beloved 30-Pin.