That's not what TOS did though (and TOS was supposed to be a Deep Space Mission away from civilization), TOS would pull out new characters for episodes and act like they were always there and long crewmembers. No one minded this.
The original Enterprise
had around three times the crew of Voyager
(150-ish to 430), so they had plenty to spare. Besides there will deep space stations (such as K-7 and others) where they can restock supplies and take on new personnel, Voyager
never had that option (except then they took on a handful of people from the Equinox
), so the producers/writers/PTB should have been far more involved with the ship as a whole.
It would be easy enough to create 150 names and add to the series bible, so that the whole crew was accounted for from the very beginning. I've done it for a fanfic on a ship with 126 officers and crew, its not that hard--easier if you have a small team of people working on it. It would help add a sense of "realism" to the series, make the ship actually feel like a community bound together by shared experience and regular life-or-death situations.
But then again, after Seven came onboard they couldn't be bothered to do anything with most of the series mains, so all the little people were pretty much screwed of getting anything of worth.