^Well, there are Emergency Holograms of the three types in STO.
But there are additional points:
1. What is the difference between regular (entertainment) holograms and dedicated/professional holograms?
We have seen regular holograms that were the same as the real person. So why can't I just create a holographic McCoy and let him heal people?
2. The problem of "memory"/"run time". This is connected to my 1. point. The longer a hologram runs the more unstable it becomes and requires a restart/reboot - kind of like Windows.
A regular hologram has a run time of a month, a emergency a year and the long-term five years.
So you could have a emergency hologram on ships within or near the UFP. And a long-term on explorers where the hologram cannot be restarted because it needs the knowledge on the new species encountered on the current mission.
This was the problem with Voyager's EMH, they could have restarted him, but as it would rob him of his memories they searched for a different way.
3. Why there was a Medical hologram, well perhaps Zimmerman had to create one because Barcley's hypochondria was getting on his nerves. And if the Medical one would have been successful, he would go on to create different types.
4. ESecurityH, just what weapons would they have? Holographic phasers? Could a holoemitters handle so much power?
5. Reachability. Already the Prometheus had holoemitters everywhere? But is accessibility the only requirement? In Engeneering: Perhaps it is faster for a human to just jump to his death and press the button to release something then it is to call a EEH and explain to it what it should do.
6. Human in the machine. Something we have seen in M-5 and EMH (just basic arrogance, at the time when he adapted too many personalities). At the same time what constitutes an emergency...
7. AI rights. If you give human rights to AIs, just how do you create more an actually use them?