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I really see no appeal.
If you have a ps3 it already streams everything and you can play its huge library as well as all the games it shares with Vita.
If you don't have a ps3 it costs 150 dollars (50 below a ps3) and way above a streaming device.
You might not see the appeal, but others do.
I agree about pricing - $100 for a decent video streaming box isn't that expensive or unusual, but not including a remote of any sort at that price is a bit misleading. DualShock controllers aren't that expensive if you look around and/or buy used... but the difference between $100 and $150 is significant for this type of hardware. If Sony found a way to include a remote (maybe for video only) at the $100 price point that would be a huge addition.
But games are a great value add, and really set this box apart from other streaming options. While you might not be impressed with the library Vita does have an increasing number of solid exclusives and a nice (limited but growing) back catalog of supported PSOne Classics.
Being part of the PlayStation ecosystem also makes it an easy sell for many people. If you already own games on PSN (or for Vita) then you have stuff to play immediately; if you already have a DualShock controller then the initial buy-in is lower; if you plan get a PS4 then the Vita TV offers some cool extra options for a second screen.
Finally, comparing it to systems that are older and about to have support cut off isn't really fair. This system has a library of games available now and will continue to be supported in the future. It also is still significantly cheaper than any option you mentioned except the SD, non-HDMI compatible Wii.
There is a market for this product. You might not be part of that market, and I have no idea how many people actually are... but it does exist.