Imagine a ship full of holograms with the best possible qualities-Janeway and by extension Starfleet are nervous about that because it would render them obsolete.
Until that ship is in battle and the holodeck power grid is knocked out, making the ship suddenly empty and ready to be commandeered by the attacking force.
Overall, in an in-universe sense, the more I think about it, the more I don't like the concept.
I still think its usefulness is limited, and given the constant problems that Starfleet crews seem to face with the holodeck, I'm not convinced the technology isn't far too brittle.
Even if they were to do an ECH, it really shouldn't be the Doctor. While he's off commanding the ship, he can't be simultaneously treating patients. Presumably, if the ship is in such dire circumstances to need an ECH, there are probably a lot of critically wounded people that also need attention.
An ECH doesn't really need to be a hologram either, but would function much better as simply an automatically enabled computer program with no physical parameters. There's no reason to waste the energy to project it anywhere - it just needs to be tied into the primary systems and have command execution authority. It's primary function is the capacity to make sound strategic, tactical and ethical decisions based on available evidence from the sensors. It has no reason therefore to interact with its environment the same way a Doctor, or an Engineering Hologram (Reg Barclay?) would.
IF they were going to go ahead and make it a hologram, then it should be a separate hologram from the Doctor. The more you add to the program, the more likely you are to introduce errors. Additionally, I wouldn't want it to look like the Doctor so that the two could be clearly distinguished by more than just a uniform color.
From an entertainment / ratings perspective, ECH would have been a great way to give William Shatner a special guest star, 1-off appearance in Voyager, if they could've managed it. It's very plausible that such a hologram would be patterned off a dead historical "great" & being the late 90's, he wouldn't look that much older than Generations, and it would a big ratings stunt for them during sweeps. That's pie in the sky thinking, but still fun (for me) to imagine... though I'm not sure Shat would've looked great in a Voyager jumpsuit.