Why would Activision sell it?
A dead franchise that would be extremely difficult for them to revive on their own without completely fouling the IP. It would cost a fair bit and would be risky to pull out; would be hard to predict the success of Skylanders design working with Crash in some way.
Also, money. If Sony offered $500m for example, that is a large cashflow with no effort but laying on a dead IP.
Why would sony spend 10s of millions buying it when it wouldnt sell that much anyway?
That's purely conjecture that it wouldn't sell much. With a sufficient marketing campaign, a brand new Crash Bandicoot on PS4 could sell a lot of units worthy to justify a large cost to acquiring the IP, especially at Christmas time aimed towards the family market, which Sony plans to target more towards in 2015. The brand recognition for Crash Bandicoot always reminds people of the PSone days and Sony were keen to push that during the PlayStation Meeting in February 2013 when they announced the PS4; this experience event is definitely giving me vibes of that too after Sony posted the Vine's of the PS1 and PS2 bootup screens with sounds and the picture of the PS1 memory cards with #memories.
Who would even make it? Everyone from that era of Naughty Dog is DEAD no longer with the company.
That's not to say another creative team at Naughty Dog couldn't create it, but want to know whom I think would be second best? Media Molecule.
Edit: Just to add one more thing. Naughty Dog did give a nod to Crash Bandicoot in their Uncharted 4 trailer with the animation, and the narration by Sully could be referring to both Uncharted 4 story, or doing a Crash Bandicoot "...one last time, for old times sake".