In my opinion, the central conceit of Warframe—that you are a Tenno, whose most pivotal power is not destruction but connection—works much, much more effectively when Warframes are interpreted as full beings in their own right, and not just "meat suits" with mere echoes of personality remaining.
For game design reasons (i.e. blueprint acquisition, Helminth system, they don't want to produce unique AI and scripts for every Warframe), they must all be treated as game items, and there have been attempts to explain them in canon as inanimate, Tenno-made replicas. And I'm not saying that this shouldn't be possible at all or that you can't tell that story. It's just not the only way the game of Warframe can or should be interpreted.
The gameplay is about Warframe combat, but the thematic point is that Warframes (and their Tenno) are not mere weapons or tools. That's what the Orokin wanted, and it's why they failed. The Orokin wanted Warframes who were bodies without their own wills, mass-produced responsive war machines. They never got that. Warframes are certainly animalistic, but they are also intelligent, with mannerisms and thought patterns now alien to humans. They can spiral into Infested madness without help, and the solution is for a Tenno to meet them where they are, as the no-longer-human but still person they have become.
Transference is to connect with the person that the Warframe is, to "see inside an ugly, broken thing—and take away its pain." If every Warframe our characters use (save Umbra) is merely an echo of a dead person, they no longer involve this present compassion and care. They no longer channel the essence of what being Tenno means. You can still sprint, bullet-jump, and fire off abilities in an inanimate Warframe, yes, but thematically speaking, that's not and never has been the point.
Warframe is about the power of connection and love. Transference, on its deepest thematic level, is love. It's a Tenno stalwartly acknowledging a Warframe's personhood, communicating with them and taking their needs seriously even when it's not straightforward. It's a Warframe entrusting another with shared control, holding their Tenno close in their very body as they fight in tandem.
Great storytelling comes from embracing, accepting, and confronting the idea that Warframes are beings with their own needs and alternative methods of communication. Both Tenno and Warframes were once merely human, but have since transformed into something both "more" and "less". Their extraordinary abilities come with deep scars and a fundamental disconnection from their former kind, whether that's due to ageless immortality or physical transformation. Most humans can no longer understand what they've been through. In the wake of this ruin, they reach out to one another.