I'd love to see Elena back in competitive skating as she is one of the most talented female skaters ever.

However it would be a long shot for Ilinykh/Soloviev to become a competitive team.
It takes a good 3 years for a team to gel properly and to build an ISU ranking.
They have a slight head start having already skated together in shows, but would need to be knuckling down to some serious hard training pretty soon, to have any chance of having programs ready for the test skates.
This doesn't appear likely, as Elena is clearly not even in Moscow.
Also Elena has been out of competitive skating for some time now, and it is difficult to return to the extreme discipline required after such a long time.
There would additionally be the problem of who would coach them, as they would not be coming back to play 2nd fiddle to S/K. I would doubt too, that Zhulin would be prepared to take them on given the history between Elena and Nikita.
If Elena could bury the hatchet, Morozov would be a great choice. Morozov is a genius when he puts his mind to it. If anyone could launch a new team straight to the top, it would be him!
There is also the fact that Soloviev is no spring chicken
(almost 30) , and even Elena might feel that as she turns 25 this month, she is a little old to start again from scratch.
Another factor would be that they would have to play catch up to the 2 top Russian teams, who are now both firmly World medal contenders. That would be a tall order.
Though never say never, it would be so much fun if they did team up. Ice dance has certainly been less dramatic without Elena!