The real reason Marvel's best Phoenix hosts share the same power
The X-Men's Phoenix Force has always seemed to show a penchant for telepathy - and teenage Jean Gray understands why that's troubling.

There's a dark reason why the X-Men's Phoenix Force tends to seek out telepaths as its hosts. The Phoenix Force is the cosmic force of death and rebirth, the nexus of all psychic energy throughout the Marvel Multiverse. It serves as the guardian of evolution, burning away the forces that hinder change and growth, unleashing the potential for change and mutation. This is why the Phoenix has always had a special interest in Earth, given the unparalleled potential of humanity.
The Phoenix Force has had many hosts throughout history, but a surprising number of them came from Earth. The best hosts in Phoenix are psychics, most notably X-Men's Jean Grey. For all her powers, the greatest Phoenix host—the only one who wasn't quite in Dark Phoenix—was Rachel Gray, a Phoenix-born woman of her time The line was later avoided. Like her mother, Rachel is an Omega-level psychic herself.
The Dark Reason The Phoenix Prefers Psychics

The Phoenix Force's preference for mediums is explained in Jean Gray #2 by Dennis Hopeless and Victor Ibanez. Time-displaced maiden Jean Gray senses the Phoenix is coming for her, and She turned to her previous owners for guidance. Telepath Quentin Quire welcomes Jean into his own mind, where he reveals that each of the former masters has been psychically wounded by the experience; kind of harm. People who do not have this kind of strength are naturally at a disadvantage and are prone to willfulness.
Marvel's newest Phoenix host is Echo, a member of the Avengers, who will likely need her friends by her side when the experience is over. Echo has never had powers like the Phoenix Force before; she's not even a mutant, let alone a telepath. Apparently, Echo isn't her first Phoenix bloodline. A dedicated Echo miniseries revealed there were other Native American hosts who appeared to be among her ancestors. But no matter what, Echo will find herself in pain when the Phoenix Force leaves her, as its flames will burn her mind, just like Rachel Summers, Quentin Quire, and Colossus.
However, the interesting question is whether Jean Gray is actually an exception. Jean is an Omega-level telepath who seems to be related to The phoenix is on a level akin to apotheosis, the two effectively becoming one. This could very well mean that the X-Men's greatest telepath is the only one who can safely wield the Phoenix Force.