Geordi was retroactively described as having impressed Picard with his engineering skills originally ("The Next Phase"). Perhaps "flying the ship" is make-work for people who can't get a real assignment, because all ships fly themselves anyway. Or more probably, starship pilots are picked from shuttlecraft pilot pool, and shuttle pilots are similar to today's truckers: expected to be capable of maintaining their vehicles.
the only assignment available to him was Transportor Chief, especially because he was a non-com.
This is the one thing that remains rather difficult to explain about Colm Meaney's constant rank identifier changes in the various shows. Dialogue basically agrees that he always was a noncom and never attended the Academy - so how did he become the Tactical Officer of the Rutledge
I can understand that the position could carry a formal name that is unrelated to the exact nature or training of the person holding the position. But Tactical Officer is something of a bigwig on most of the starships we see - at least a Lieutenant on Kirk's and Picard's ships. Why would Captain Maxwell take a Marine Sergeant, no matter how accomplished or how many times the savior of Maxwell's own bacon, as his TO?
Sure, the Rutledge
could have been a fairly small ship, and perhaps was stranded behind the lines far away from crew rotation if the Setlik III nastiness resulted in a military conflict of some scope. And the incident where O'Brien had to save a landing party might not have ended 100% well, meaning that top officers (typical landing party members) would be casualties. But still... We don't have a good reason to think that the big war with the Cardassians started in 2347 already, and we have a backstage reason to think that Maxwell's ship was at least as big as Kirk's, with plenty of commissioned officers to choose from.