Also, I don't get the part where a program running in a computer somehow has to be an integral part of the entire computer, acting as its avatar or whatnot. That's not how computers and programs work today: if my multi-thousand-page treatise on starships somehow began interacting with my multi-thousand-page treatise on ponygirls, let alone with my Spore or LightScribe or Skype, there'd be something seriously wrong with my PC or my cloud or whatever.
My initial point was that the program inside the computer is not going to be smarter than the computer. The program is part of the computer. Reg wasn't arguing physics with Einstein, he was arguing with the computer. The Einstein program was not smarter than the computer as the computer contained all the knowledge that Einstein hologram had access to. Heck, by 24th Century the computer should be smarter than Einstein - at least it should have more knowledge and applied data.
No, your starship paper won't interact with your My Little Pony paper. However, your Starship Combat Simulator is going to use X amount of computer processing and so is your My Little Pony interactive world program. They both use the same computer core and processing capabilities. They both use the same graphics accelerator. If one of them starts becoming a memory hog, the other one will not run as well. Heck, one of them might even cause an incompatibility issue simply by being installed and the other won't run at all. Also, some smart programmer might be able to write a patch or script that will allow the two to interact with each other.
It was one starship computer with one overall network. Sure, the Holodoc was an independent program from the navigation controls, but he was still a computer program resident on the same computer that those navigation programs and replicator programs and all those other programs were on. I'm not saying he should or must or would automatically have access to all the other systems, but the potential is there for him to be able to instantaneously access the data and information. This is the same way that an app on a smartphone today can instantaneously access the GPS system, access the mobile network for the weather and time, pinpoint where the good restaurants are on your route and let you have interactive chat with people on your contact list. Integrated apps that communicate between each other are common now.
But it wasn't Einstein. And it wasn't Leah Brahms. Of course, that was the point of "Galaxy's Child," that it wasn't Brahms in "Booby Trap."
And the doctor should have been able to have multiple copies of himself running at the same time the way we today can have multiple copies of the same program running on different computers at the same time. It might bog the system down at some point but 2 doctors at once operating on a patient would probably have been well within the processing capabilities of Voyager's computer. Or one doctor treating wounded on the bridge while another is treating wounded in engineering.
1 organic and the rest of the crew holograms? Yeah, I'm in the camp that it might not be good psychologically.
I'd much rather see a biological crew with 1 holographic member that is an avatar for the entire ship's computer.