The transporter's "abilities" have often been shown to be quite extensive. Essentially we've been shown the transporter is a fountain of youth.
You've got the situation in "Rascals" where components of Picard's, Guinan's, Ro's and Keiko's DNA linked to aging are removed turning them into children and it was determined that they'd just simply age normally after then. So, basically, all one has to do is run himself through a transporter, remove that component and voila
you start your life over from adolescence.
Then there's "Unnatural Selection" where a gentic experiment giving engineered "children" an active immune system leads to Pulaski and others contracting a virus that caused rapid aging by mutating DNA. Pulaski was "cured" by running her through the transporter and "filtering" her with a sample of her DNA pre-infection thus making her young again. (Well, "less old."
Now granted, there's "real-world" science problems with both of these situations as your age isn't programed into your DNA. But in Trek's "science" there's some component of DNA (or other body cell) that is linked to DNA and manipulation of the transporter can take advantage of this.
Screw the Briar Patch! Star Fleet has a fountain of youth installed by the dozens in each and every one of their ships, bases, and facilities. Just have someone keep a sample of their "DNA" from a time in their youth or just remove their "adolescence cells" and they can live their life over again!
I guess it's possible people in Trek's time (and there's much evidence to this) that people are so greatly advanced and enlightened that notions such of these are pretty much out of the question. But, still, the option is there. If they can use Pulaski's DNA as a "filter" to cure of a "disease" and restore her to normal then they should be able to cure almost any severe illness someone could contract.
There was even an episode where Picard beams himself out "energy only" and later is resurected (using his own body's energy) and the transporter's trace to restore him.
I think the Transporter has been given too much power in this manner.