I have been seeing in lieu of Sony's ongoing profiting issues, that people say that the playstation divsion could simply spin off into its own thing or be bought out. I get the impression that a lot of people are okay with this scenario, but i see some issues with that. 

One being that there will be a lot more studio closures and/or layoffs. This would great constrict all of the new ips they make.

Second point is about Playstations ability to have a wide berth of distribution and advertising without the resources and connections that Sony has.

Lastly, all of the potential companies who would be able to financially secure the playstation division, are far more interest in the mobile market or their own micro console. 

I liken this response to the "they should become third party" argument that we hear about Nintendo

I think you made a mistake in your title. Instead of 'is', don't you mean isn't?

And I agree with your points. PS wouldn't be able to survive on its own. At least not with its current business model.

Agreed.

The Playstation division being spun-off from Sony would probably have little to no impact to the consumer. It's an action taken for investment purposes. Still, it would make more sense to spin off the parts of the company that aren't doing well or that have unpredictable results.

As for selling off Playstation, I can't imagine that happening.

All the money made by Playstation is currently lost by the other Sony divisions, Playstation would have much more financial resources to invest in games and players when being a single, independent company.

But the shrinking Japanese market with less children being born and a steadily decreasing population will force them to merge with Nintendo anyway, since there is no space for two console makers in the Japanese market.

As a consumer of the big three the worst hardware maker is Nintendo.

I do not have a problem with the idea. I just do not really see a reason from your points,

In my view, PlayStation's fate is tied with Sony

Okaaaaaaay. That doesn't matter, Neither Nintendo nor Sony are rely on Japan.

The point is. Playstation is sony and sony is playstation. They'll only seperate when sony goes down or when their gaming department becomes outdated like their pc department was and sony decides to sell it.

Also when playstation was on its own when the ps3 launched I wouldn't be sure if they were still around in the form we know playstation in.

No. Not at all.

The Playstation division can use the resources and talent of the other consumer electronics divisions. It is no easy task to design good hardware - take a look at the much bulkier XOne.

As soon as such designing experience isn't needed anymore the Playstation brand has to go "virtual" or will vanish. Because everybody will then be able to use some PC-hardware (maybe an NVidia, AMD or Intel reference design) and sell it as an settop box or console.

At this point the OS is "king". Microsoft has no problem selling a "Windows for Games" reassembling the XOne experience as the XOne is already running Windows.

As soon the Linux based Steam OS or Amazons Android based consoles gain enough market share Microsoft will counter them.

Sony can't as they neither have the experience nor the resources to get their OS up and running on generic PC hardware.

The new generations of GPUs will soon make the XOne and PS4 look even more outdated as they are already. It is just a matter of time when the "real" Next-Gen hardware will become affordable to the console customers.

Expect this to happen within 2-3 years.

Microsoft and Sony knew this when they decided to go the "cheap" route. This generation offers the least amount of power for the money compared to the PCs when launched. And both are not that heavily subsidized as the lifespan is expected to be much shorter then the previous generation one...