Oh, I totally agree -- hence the "can of worms" comment.
In a society like the Federation, if you can produce completely sentient holograms more or less at will, then what is society's obligation to those holograms? Should they have the right to "chart their own path?" Potentially displace others from their careers? Since they can be tailored for particular jobs and have stamina, abilities, and such far beyond most organic species' level, and never die, and can theoretically be upgraded as time goes on ... is it fair to allow them to potentially rise through the ranks and take over organizations like Starfleet? What happens when they outnumber the organics? Will it be the Eugenics wars all over again?
I'm sure these are the kinds of questions that were asked when the EMH started fighting for holographic rights, and I'm sure that debate would last for years. Given the general ban on genetic enhancement, I confess I'm not optimistic about the results of his efforts. I can see them treating him as a special case, much like they treated Data -- but more than that ... I'm just not sure.
Anyway, for purposes of this story, "our" EMH is definitely still around (on Earth, for now), but Bashir and Co. are the doctors on the Tesseract