You cannot teach kids - or anyone for that matter - the relatively simple concepts behind programmable automation with a PC cheaply since the two main IO ports with a decent history and user configurability in them have all but disappeared (Parallel and non-USB serial ports).
You can demonstrate automation on other devices such as PICs and Arduinos but you can't actually program them without an external PC. (True that you need to transfer the OS to an SD card for the Pi but once it's done, the PC is no longer needed. You can hardly say to a mate "Hey can you let me compile my program for my PIC on yer PC?" - it's not quite the same in terms of time and inconvenience)
The cheap PC being touted may
have the IO ports I mentioned, but are typically not very 'green', generating a lot of heat, are noisy, and generally if the power supply needs replacing, it costs as much as the PC itself. This is before the extortionate cost of suitable RAM and hard-drives one finds when trying to rebuild a PC wgich is more than three years old.
The Pi in some sense can be viewed almost like a cartridge-based console, given that you can keep an image of whatever OS/distro and setup you desire on multiple SDs (a good example might be swapping between XBMC and Wheezy).
It's not that such PCs - and I like my PCs - can't be useful but if I had a choice between a hulking great box and something the size of a wallet to perform the same task - say a router (I'm thinking of Freesco-style setup here) - then the wallet-sized box would win.
There's also possibly some kind of weird nostalgia trip on my part as a 20 y.o., I used to mess around with my VIC20 back in the early 80's for more than just games (DIY expansion board, DIY expansion of 8k module to 16k, use the user port to drive a PLC output card, etc).
The Pi offers everyone to opportunity to learn while they play - or is it play while they learn? - in a manner which is "non-threatening" on a number of levels (size, expense).... and you can more easily afford more than one if the need arises