It depends on how anal you want to be about "Unique". Sure, the Rebels have Sabine's TIE, but other than that, the "TIE Only" restriction makes an upgrade effectively Imperials only and still covers well over half their fleet at this point in the game. If FFG wanted to buff the Imps and not the other factions, a few more TIE only cards would be the way to do it, and they could go in specific slots to buff specific ships - a TIE Only System or TIE Only Tech - even something like a TIE Only munition would give them a lot of specific targetting capability.
And yes, you can decide that Sabine's TIE makes that "not unique" to Imperials. But that's not a sensible argument. As has been brought up, literally only one slot in the game is unique to any single faction - the original astromech slot. And that is only unique because FFG put out a bunch of early astromechs, most importantly R2-D2 without the "Rebel Only" limitation. Otherwise they wouldn't have bothered with a whole new slot - they would have just had "Scum Only" astromechs instead of Salvaged Astromechs.
I think at this point the likelihood of new, faction specific slots is very, very low, and retroactive slots even lower. Tech made sense to distinguish ships from the GCW era from TFA and beyond era. I could... conceivably imgine some sort of "antique" or "vintage" slot that went the other way, if they decided to bring in ships from the Clone Wars, but the fact that the Y Wing, Z-95 and most importantly the ARC are ingame without them means it probably wont happen.
One plausible way we could see "new" slots opening up would be the migration of a few more epic slots - cargo and teams could make their way to the 100/6 game. Krennic's shuttle might benefit from a Death Trooper team, and it would almost seem silly not to give the Rogue One Cargo Ship a cargo slot if it makes it into the game. But neither slot is likely to be unique to one faction or another, except possibly in the short term.
There are other ways to balance Imperials without adding a new slot - it's not going to mean the Imps are permanently locked out of the top tables (" the long term balance of the game", as you put it, is definitely not at stake). Partly it'll mean FFG releasing new upgrades that recognise the balance issues and do something bout them, just as they always have(to varying levels of success). Partly, it'll mean releasing different sorts of ships going forward - ships like the Silencer and the TIE/sf seem to be, at least in part, the result of FFG recognising that 3 health behind three agility and a reposition action just isn't a viable survival strategy any more, with bombs and turrets now part of the game in a big way, probably forever. Partly, it'll be Imperial players recognising the same thing that FFG apparently have, and giving up on Interceptors and TIE swarms the way Rebel players have had to give up on B Wings and Trip X Wing builds. They're remnants from an older era of the game. Adapt and move on, or stay back and play casual tournaments. Both are good options.
I'm not saying Imperials are in a great place right now. The data makes clear that they aren't. But, with the Rebels now hit with the nerf bat the way the other two factions have been, there are Imperial options again. New Kylo. High PS alpha strike. TIE/D Defenders. Kylo/RAC and an ace. Wait for the post FAQ meta (and especially the post wave 12 meta) to shake out before declaring that Imps are dead without a special new slot.