While there is zero proof of this, I would like to speak conjecture:
The Phantom was introduced as part of Zelda's initial 10 screenshots because it may be part of her moveset. The Phantom is iconic to the series for representing the first playable excursion with Zelda; had her spirit inhabited the suit of armor, it would have glowing pink eyes, but this is not the case. Phantoms can appear and vanish in a second, so it's not farfetched to assume Zelda, a canonical controller of Phantoms, can summon them. The delineation between Link and "Toon" Link is for the sake of having two different Links. The Phantom was introduced in, and pertains solely to Toon Zelda. Because the revealing of the Phantom has not also revealed the [now less likely] newcomer "Toon Zelda", her chances of appearing are extremely slim. I feel this is because the Smash team considers all Princess Zeldas, regardless of depicted art style, to be congruent.
Is it so remote a concept that Twilight Zelda could display abilities introduced by other incarnations of the princess across the series? As far as canon goes, Sheik is only relevant to Ocarina of Time Zelda. Tetra is only relevant to Wind Waker/Phantom Hourglass Zelda. The Phantom is only relevant to Spirit Tracks Zelda. Yet, Twilight Zelda (as our Smash Bros. version appears) transformed into Sheik in Brawl, a trait belonging only to her predecessor Ocarina Zelda. Sheik may very well return for a second appropriated outing with Twilight Zelda in SSB4. Why is it farfetched to assume The Phantom may become part of Twilight Zelda's moveset as well? Because it's from a "toon" game? The art style is irrelevant. That said, I feel Toon Link could/should have been called Young Link.
My argument is not in favor of Impa at all. That is a related, but distant conversation piece that has no true merit yet. This is not the time to discuss Impa for we've no evidence to suggest she'll be in the game. While I favor her inclusion over Sheik, we should really only discuss Zelda and the Sheik potential for SSB4 until further notice.
The discrepancy between Zelda's angry "beckoning" pose in the discussed two screenshots: The Phantom/Fox and Link/Peach is a curious point. There's not enough available information to draw conclusions, but considering the fervor in Zelda's facial expression, it appears to be an attack of sorts, not a taunt. It appears that her hand gesture is portrayed in a 'commanding' demeanor, as if she's issuing her Phantom defender to attack. I will repeat: Phantoms can be summoned from the ether. It is possible in the Link/Peach screenshot that the animation frame was caught prior to the summoning of the Phantom—or even less likely, that the Phantom was summoned at a greater distance beyond the view of Link and Peach.
The truth is, Sakurai and co. could choose anyone for the role of Assist Trophy. Phantom Zelda is an assistant to Link in Spirit Tracks, so it is a somewhat fitting AT. The concept was introduced in 2009, a year and a half after Brawl was released and far beyond the development of the game to include any such idea. The series that Smash Bros. sources change over the years and The Legend of Zelda has done some neat things with its Princess since. The Phantoms in Phantom Hourglass were mere enemies, while in Spirit Tracks Zelda's spirit was able to possess them to help Link. Because she had dominance over their stature, she may very well possess a new ability to summon them in SSB4. To note: while playing Spirit Tracks, you could draw a line from Phantom Zelda's location on-map to Link's and she would warp to his aide. You could summon the phantom.
In PH and ST, when Link is spotted by observers, Phantoms would appear near and begin pursuing him. In some cases, they could appear in his immediate vicinity and without quick evasion, would slash and kill the hero in 1-2 seconds. One of the key characteristics of Phantoms are the ability to appear and attack quickly.
As mentioned before, this Phantom attack appears similarly to Yuna's quick-summoning moveset from Dissidia 012 Final Fantasy wherein she, using her summoning staff, would attack on the fly with the likes of Ifrit, Ixion, Shiva, Valefor, and Bahamut depending on the executed move. These aeons would appear out of an instant rift in space, their top halves protruding from the hole to deal damage before disappearing as she moved away. Incorporating such an aspect into Zelda's moveset without taking over her conceptually would only EXPAND on her potential as a spacer.
We're all equally guilty of idiocy for assuming The Phantom is an attack or an Assist Trophy. There's no way to know right now.
My two cents on the potential.
Edit: There is the lack of the Phantom pic appearing as one of her listed specials on the Miiverse site. Not every characters' specials have been revealed, but where pics are appropriate they have. Sakurai's either holding out, or it's an AT.