It's been quite a while since Rachel Summers made an appearance in the X-men, and we're probably not seeing her any time soon. There's a few ways I can back up that statement, such as the fact that she hasn't been brought back already (which means she is either a) somewhat unpopular, or b) already scheduled to appear as part of another story arc yet to come, but even if that is the case, there's so much going on in the Marvel universe right now that there just doesn't seem to be much of a place for her), but I'll stick with the most interesting reason here, and say that she can't exist in the series (as Phoenix, which she has been since the mid-80s) for as long as Hope is around. And I don't think Hope will be going anywhere for a while.
Why can't they exist together? Simply because of the fact that (and I'm finally admitting it) Hope is probably channeling Phoenix power in some way, either via mimicry or something else, and a large part of the legend of the Phoenix is that there can only ever be one at a time. In myth, it lays an egg, the only egg it will ever bear, and dies, right on top of it. All phoenixes are, therefore, orphans (Kinda like Rachel), and the sole member of their species for the duration of their life. Note that this also means that Phoenixes reproduce asexually, but that's beside the point.
Think about it, when have you seen the Phoenix being channeled by two different people at the same time? No, the Stepford Cuckoos do not count, they're essentially a singular entity. Sure, Jean Grey and Rachel did happen to be alive at the same time for a while in the 90s (I think it was a little after Inferno, notable events therein included Scott and Jean's wedding), but were they both Phoenix at the time? I don't recall that being the case.  
So yes, Marvel did, indeed, go with the obvious and make Hope a Phoenix avatar of one sort or another. Personally, I find her the most likable host in the series to date. Jean always struck me as being too perfect, and Rachel...I never liked Rachel. Even if this is the return of Phoenix after a glorious few years of respite, it's with a new host; one that has still uncharted levels of power (well, they always say that...). We're not facing another 'oh look, Jean's back....again' scenario, we don't have to listen to Rachel yell at Cyclops for not creating an Earth 616 version of her (I always thought that was super creepy...), and best of all, no Madelyne! I, for one, am pretty excited to see what lies ahead for the X-men.
 
(Also, feel free to correct me, I am by no means an expert when it comes to the Phoenix Force)

There is and can only be one Phoenix. The rest are shoddy, obvious marketing ploys that I can only Hope will continue to fail miserably. 
 
Suffice it to say, I thought Warsong was completely hilarious trash. Endsong sold better for an obvious reason, but here goes Marvel trying again. We didn't care that the Cuckoos had the Phoenix, why should we care that Hope has it? 
 
 
The real thing, Marvel, please and thank you. 

" Yes, and that only one is Jean Grey. "

There is only one,  and that will always be JEAN.  
If i had to say there was a 2nd, then the logical choice would be MADELYNE. 
Next would be RACHEL or maybe even CABLE. As Jean's (and Madelyne's) offspring, the power is their birthright..  
HOPE is powerful, but has no direct claim to the full power of PHOENIX. 
There clearly can be many Phoenixes but Jean isTHE PHOENIX.

The Phoenix has had two host at the same time, it was in Rachel and Maddie (which became evident during Inferno), Jean absorbed the piece Maddie had and unleashed to destroy the hand of Celestial.