In particular I'm talking about the PSVita, since the PS4 is a juggernaut already.

The PSP is the best selling non-Nintendo handheld, being the only real competitor (excluding mobile and tablet) to Nintendo's control over that market. Part of its charm was a software that allowed to create homebrew with ease. And even with the massive piracy on the device, it sold enough units to attract a lot of developers to create an unique library of games. And let's be fair, other easily pirated machines (like the DS, Wii, PS2...) have sold a lot of units as well thanks to that appeal.

Looking at the PS VITA,it's the system that has suffered the most since release. It has stop selling in NA, barely sells in EU and it can barely compete with the 3DS in Japan, and with the N3DS already on stores there, the gap will expand. 

I don't know the numbers of the benefits that Sony gets from the system as a whole, but I'm sure they're not good. So why not allow the PS Vita to receive a similar status as the PSP? If piracy is an excuse for publishers to not support a system, maybe they would change their minds after the Vita gets some sales. Sony doesn't make AAA titles (I don't think they make even games for it, but I'm not sure about that), so the lost videogame sales would be compensated for the hardware. I don't think the Vita can recover at this point, but what if they had that strategy from the begining?

As long as the hardware is profitable, sure.

Piracy sucks for everyone except the pirates. No.

no not sony
only the Hardware sales. but thats not what benefits sony the most

Most certainly, if they can make profit on hardware - PS1, PS2 and PSP are pretty much proof of that.

Not even piracy can save Vita, because it doesn't have any games worth pirating... Doubt that westerners, and especially Eastern Europeans or South Americans would buy the system for indies and niche Japanese titles...

Yes, but if the software allows homebrew, it can be used as an emulator. How easy creating a PS1, PSP, N64, SNES, Génesis, NES, DS, GBA, GB... emulator can be? The Vita is already capable of using a PS1-PSP emulator, so that would give it a HUGE appeal to retro gaming.

You are correct. But somehow I believe that majority of pirates do it for the current games, what you are proposing is still aimed at a small minority of hardcore gamers.

The value of piracy is attracting casuals to buy your console, the casuals who would usually only buy one or two games and don't see the value of investing...but with an endless supply of free games they are more willing to spend an initial $200, or even $400 for a home console...

And Vita simply doesn't offer that...

This^

If Sony makes tone of profit out of the Vita hardware (including marketing to sale it, etc...) then it may not be that bad (be even this is very doubtful)... But good?  no.

Other than Pirates themselves repeating (and believing it) that it is good for the industry, everyone can easily undertand how bad it is for the industry :(

Edit: Edited my post, as I did not want you to believe I was attacking you in any way by asking where you got that impression pirating could be good for the Vita. Your OP explained it very well :)

no, it wouldn't, they make their money from software