@JRPG: PSii would be a logical name. It would match Vii and Wü pretty well. Also, Sony could say in its PR that it has improved parapsychic gaming in it.
There are a number of reasons why Sony won't do it, one of them would be the resources required to support new platform.
If Sony would make the PSii; as i said in my previous post, 3rd parties have hard time to grasp the idea behind the Wii, which would mean that Sonys own devs would need to push the PSii and the resources would be taken away from PSP and PS3 developement (then again, if PSii would turn out to be successful, Sony would be able to ditch PS3). When we look at Wii, we'll notice that it lacks 3rd party system sellers completely, and there is no reason to expect that PSii would get any different support (especially when the talk was about getting ports).
You could ask why so rare companies attempt disruption, it's because of the strategy requires dedication to the strategy. Also countering the disruption with disruptors weapons isn't any easier for the same reason. If we look at 360, it doesn't have a web browser, and a reason for this is M$ wanting to protect their core business. The lack of web browser in games console of course is rather irrelevant, but it points out the problem these companies face; your counteractive "better" product is forced to be made inferior, so that it doesn't pose a threat to your core business.
As for the hardware side, if PSii was targeted to counter Wii, it would need more simplified architecture and more power than Wii has. If the console would have BC, it would also need to have enough power to be able to emulate PS2 games. And on top of that, Sony could run into legal issues, if Nintendo has patented enough stuff in Wii Remote.
