In Voyager Season One Episode 7 - "The Eye of the Needle" - the Doctor up to that point had been treated as nothing more than an appliance and seemed to have very little rights. During this episode, Kess brings her concerns to Janeway and things begins to change. After she realizes her mistake, Janeway tells The Doctor that he has become a full-fledged member of the crew and from that moment on he was treated as the Chief Medical Officer of Voyager.
After this event, The Doctor was sent on away missions that could accommodate a hologram when a medical officer was needed. And when he acquired the mobile emitter in the "Future's End" episode during season 3, the mobile emitter belonged to the Doctor just as another member of the crew would own something... like a pair of shoes. This is why Janeway did not create an army of red shirt holograms to use the mobile emitter for away missions. The emitter was borrowed on occasion... such as the time the Barclay hologram needed it... but always with permission from the Doctor.
Bottom line, the emitter "belonged" to the Doctor and if a hologram was needed to go on an away mission it would be him. Janeway was not going to upload multiple hologram programs to the emitter... it was for The Doctor.