Here's the way I see it:
The phrase "X trapped in a Y's body" exists for the simple reason that it communicates a very, very basic idea of what being transgender might (emphasis on 'might') feel like. This allows it to be understood vaguely by the cisgender majority, who have the advantage of having their gender identity accepted from the moment they were born.
And for some trans* people, it's a sound bite which, whilst simplified, does ring true on at least some level, and so they use it to give a basic description of transsexualism to others. This is absolutely fine – people should be allowed to define their identities and their bodies on their own terms.
However, the phrase is problematic in a number of ways:
1) It carries the implication that men and women 'belong' in specific forms of body, and does nothing to combat the society-wide assumption that penis=male and vagina=female. This can have unfortunate consequences, such as people who adamantly refuse to use the correct pronouns until the transsexual person in question has 'had the surgery'. Furthermore, it erases the experiences of trans* people who cannot have or do not want surgery and/or hormones.
2) Dysphoria differs considerably from individual to individual, if indeed it is even experienced at all. The idea being 'trapped in the wrong body' implies that dysphoria is solely from a physical perspective, when often social dysphoria is just as overpowering if not more so (i.e. the dysphoria that comes about through being misgendered). And often, it's not so much 'trapped' as it is that the trans* person in question wishes to alter aspects of their body to match their inner sense of self. Fundamentally, it's still their own body.
3) It completely and utterly erases non-binary gender identities. This one needs no explanation.
4) Long story short, it's only inclusive of trans* people who feel a particular way, to the detriment of those who don't.
The problem is that it's extremely difficult to explain the nuances of being transgender, and the diversity thereof, in such a way that your average cisgender person will understand. But at the end of the day, while it's a phrase I would never use to describe myself, I definitely don't have the right to say that others shouldn't use it. If the shoe fits, wear it. The problem is that we don't all have the same feet, and right now, the shoes only come in one size...
