Well good for you I guess, but you seem to think everything exists in some kind of fantasy land where the PS4 will be in some magic bubble that doesn't affect anything else.
No, I've thought about this:
PS4 [an expensive new purchase] -> lower interest in PS3 from hardcore demographic -> eventually less of the games advertised on PS3 as they directly affect sales on PS4 - Vita games however, won't -> heavily pushing the vita (finally) leads to less negative effects on first and third party sales that would have been on PS3, without affecting PS4 sales as much. Possibly even helping it, seeing how it will interact with the PS4 - making it portable.
If they were to push it, that would be the time for attempting to pull a much larger userbase with high investments in advertising, timed with the western price cut and games. Is that around TGS?
Vita games compare worse to PS4 games than PS3 games (which people have claimed make vita games obsolete). The fact that it is portable, especially in an age of growing handheld gaming, is the only way ps3 type/quality (and similar production cost, although probably less) games could survive when next-gen comes along making big publishers incredibly competitive to ensure their survival, even more than now. With high development costs and the general market's habits leaning toward handheld, Vita will cover the PS4's ass for Sony. But right now it's just moving sales from one column to another and marketing etc would be somewhat wasteful, given the initial uptake wasn't as much as they thought.
Wii U likely won't be reaching this market. Gamepad helps but it's not going to get the support PS4 will have, nor will the gamepad stream next-gen games like the vita+ps4 will universally. A different demographic will still find it appealing, but it shouldn't hurt the vita. The next xbox might if people become less convinced handheld gaming is even worthwhile. But with companies dropping out, pickings might be slim. You might have to enjoy the convenience of portable gaming.
PS4 games will also be expensive. FPS, action and adventure is ps360 dev's bread and butter - it's left to the vita eventually since ps360 hurt nextgen sales more than they are worth down the road and we know about wii u with these games.
So, this only happens when the userbase buying games shifts to next-gen games, for the time in-between, Vita becomes more relevant for multi-platform ports, possibly later seeing more Vita upscaled games on PS3, encouraging the userbase to upgrade even more like we saw from psp to ps2.
Provided Sony push the Vita more when the PS4 is out.
Not everyone has to buy everything. But the option for handheld is there if you want it. It will also be a nice place for indies and some publishers to make reasonably priced games that aren't next-gen's AAA!
Its relevance will only grow as I see it. I'm sure Sony sees that too, they're just modest and more cautious now that they've had to give up their bonus.
That doesn't make sense either since the install base won't be there which will dissuade third parties from developing for it which means even should you later decided to relaunch it, it would solely be on the back of first party games and even should the relaunch be successful it'll be a year or two before renewed third party support starts materializing and by that time any relaunch momentum is gone, those games most probably bomb or don't drive enough hardware sales and your back to square one.
This is ignoring the fact the Sony simply doesn't have relaunch capable first party software. Nintendo does and even they realised they had to take drastic measures as fast as physically possible in order to save the 3DS.
It's not that long of a wait I don't think. I'm sure they have plans for in-between. Things are going to take a while from now on I feel. Multiports etc.
Sony has GT, GoW, Infamous, Ratchet and Clank. It could by then moneyhat FF, MGS and best GTA. Infamous and killzone may not have the best pull in the PS360 market, but that's not the same as the competition on handheld.