Once launched a Trident, using a camera, gets a fix on a single specific star. It then uses the data on that star's position to correct for any errors in its internal guidance system.
There even appears to be a patent on the idea: https://www.google.com/patents/US7706917
https://en.wikipedia.org/wiki/Lockheed_SR-71_Blackbird#Astro...
First, the system would be vulnerable to many of the same problems: hacking, sabotage, and electrical failure. Second, it would likely not be as robust under less than ideal conditions in which human beings with a sextant would still be able to function (e.g., partially cloudy conditions).