The writers of Berman-era Trek never put any real thought into the whole hologram thing. A Star Trek hologram is not an entity, it's a projection. It's a program running on a computer. Other than a holodeck, which is designed to produce nonsentient holographic representations for a short term, I can't think of many situations in which a holographic character would make anywhere near as much sense as an android character. An android is self-sustained and self-sufficient. It doesn't require a whole lot of computer and projection equipment. A hologram does. Not that the writers of Voyager ever fully understood that. The EMH had a mobile emitter, not a mobile autonomous computing system. The Doctor's consciousness and intelligence reside in a computer on the ship.
That whole notion of using holograms as slave labour from later episodes of Voyager, regardless of whether they were sentient, was stupid. You can't use holograms as, for example, miners until you've gone in, created the mine, and installed computers and projection and force manipulation equipment, all of which would probably be done by programmed nonsentient robot drones, like the ones we see doing repair work on Discovery. Why, if you have self-operating robots built for labour, would you get them to do half the job and then switch to a much less efficient technology to finish it?
Let's set all that aside and assume you really, really want a holographic-crewed ship. So, how do you want to do this? Do you want to have multiple independent self-aware holographic crew members? That means a lot of computer power. On the upside, you won't need any crew quarters. All that space can be used for computers and power sources for computers and holographic projectors. Crew downtime can be spent either offline or in a totally virtual cyberspace environment. You'd probably want each holographic character running on its own hardware, so if you have a failure in one system and lose a holographic crewman, you still have others. Or do you want a ship that is basically one AI with multiple avatars under the control of the same intelligence? That would be a lot more efficient, and redundancy could still be built in.
But then you run into two issues. First, even in a Federation of seemingly infinite resources, does it really make much sense to take living crews out of the equation and introduce a lot of new hardware-dependent variables? What are the circumstances where a ship that's entirely dependent on computers would be more advantageous than a crew of living beings with a lot of computer tech at their finger-, claw-, or tentacle tips? A hologram doesn't come from a mommy hologram and a daddy hologram who love each other very much. It's not like there are holograms growing up, living their lives, pondering whether to join Starfleet. A ship with a holographic crew is going to have a crew specifically designed, programmed, and constructed for their mission. You're not crewing a ship, you're writing software. I could see possibly using that kind of ship for something like extreme long range missions, like travelling intergalactic space instead of doing standard missions within the galaxy, but even in that kind of scenario, why would you need the crew online all the time?
Second, this is the Federation we're talking about. The Federation, in pretty much every incarnation of Star Trek, has a profound mistrust of Artificial Intelligence. Yes, there's Data, yes, there's the EMH, and they both had a lot of stories about not being trusted or accepted as equivalent to living people. A whole ship without so much as a Captain Dunsel is not going to get a lot of Starfleet buy-in.
If you're going to have stories about a holographic crew, you have to have really thought through what it means to have a holographic crew, and how that works.
