My take on this is that a lot of work is performed by automatic, computerised systems. I don't think anybody in the OTU calculates jump vectors with a slide rule, or traces them on a paper chart. It's all done through a super-high resolution 3D interface.
The problem computer systems can't overcome is in deciding what it is exactly they are being used to do, and why. Humans provide direction, meaning, authorization and most importantly they take responsibility which is something no computer can do.
Furthermore there must be a lot of decisions and technical constraints actual characters in Traveller have to work within that don't show up at the game mechanical level. Laser weapons might have beam focusing, wavelength, pulse duration, recharge rate characteristics, etc that need to be tuned and traded off against each other and optimum choices may depend on the target's range, movement, materials composition, orientation, etc.
None of this shows up in the game rules, but how you ballance factors like that might depend on professional knowledge of target vessels which might vary by region or species, whether you're going for a kill or disable effect, whether you're trying to scrub armour on this hit in order to go for a penetrating shot on the next, or whether you need to go all out for max damage right now due to the tactical situation and a battle plan that's in constant flux, etc, etc. I think the assumption that one roll of the dice equals one push of a button is too simplistic.
The same goes for Navigation. I'm really not a fan of pre-computed navigation solutions you can buy at a spaceport. Putting those aside, I can imagine all sorts of minutia that might go along with plotting a jump solution. Maybe the jump vector depends on minute gravitational effects from not just other planetary bodies, but even orbital space stations or passing asteroids even millions of kilometres away. There might be 'eddies' or 'currents' in the flux of the zero point 'vacuum' energy that affect optimal jump timings. Or maybe changes in the nutrino flux from the local star are a factor. I like the rutter idea, some of these fluctuations have a rythm or cyclic nature that requires judgement and personal knowledge to ballance. Computers can calculate the details, but decisions about balancing the risks and choosing whether to trade off between delaying a jump or going for a slightly more risky jump window will need to be considered by someone that can take that responsibility.
In roleplaying games, we as players suffer from massive sensory deprivation compared to the characters we play. My character must know exactly how many buttons and switches there are on his piloting console, exactly what the benefits and tradeoffs are between using an artificial horizon or a digital HUD readout.
There can sometimes be potential contradictions in the game that need to be resolved. Pre-canned jump solutions are one, and there are many others we've discussed here. Personally my preference is biased towards saying that the best way to run a ship is with a skilled human crew because this gives you the most flexibility in how you run the ship, and rules that override that need to be house ruled or reconsidered. Perhaps they can be allowed, but with some kind of down side such as allowing pre-canned jump solutions, but at the cost of not being able to decide exactly when you make the jump, because the canned solution requires specific environmental conditions and it's going to be 2D6 hours before the 'stars are right'. Or yes you can use a computer gunner, but if you ever roll snakeyes on a roll it freezes due to a potential safety protocols violation, and can't shoot for another turn while it recalibrates. 
Simon Hibbs