Well, it's self-inconsistent, for one thing--the position of helmsman is arguably redundant, even in the way, given the computer's ability to understand spoken commands. "Maximum warp to Delta IV" could be undertaken by the computer more quickly than relaying the command to a helm officer who then types it into the LCARS interface. To a lesser but commensurate degree, the computer could replace the tactical officer as well. The computer is even apparently capable of replacing a medical officer and his or her staff, which means that the entire Science Division is vulnerable.
Need I mention TOS' penchant for destroying computers with illogic? Firstly, a series of commands that a computer cannot perform is ordinarily met with an error message and not an explosion. Divide something by zero on a pocket calculator for proof of this assertion. Secondly, a computer capable of passing the Turing test, whether through Searle's Chinese room dodge or because of its own emergent consciousness, is not likely to be vulnerable to the line "This statement is false." Check your head to see if it blew up for proof of this assertion.
I don't even want to get in to the travesty that was Voyager's Doctor, the ultimate read-only file.
Advancements I think would be consistent with the technological abilities already on display would include widespread artificial intelligences, not just a few, vast automation, actual virtual reality as opposed to the insanely energy-wasteful holodeck, and the capability to copy consciousnesses. All of these techniques exist, or at the least the prerequisites for them do, but the implications are almost entirely ignored, for the very understandable sake of relatable drama.
But, really, applying the technology they have or could have, there's little need for biological human beings any longer.