It's not accurate, as you already surmise.
Those big burners at the back strongly suggest the ships fly by pushing out reaction mass backwards to get thrust forwards. Even with future tech in mind, you're stuck with the tyranny of the rocket equation. Basically, as you go for higher speeds, you need more and more reaction mass to accelerate and decelerate, which makes your ship heavier, so you need bigger engines and more fuel, until your ship is one giant fuel tank with and engine and cabin strapped to it.
Given that, it simply doesn't make sense to go faster and burn longer than you absolutely need to. A military ship on a short range intercept mission would likely do this, but if it burned non-stop for 30 days in deep space, it would also take 30 days to undo that burn if the situation changed, so the faster it went the more it would be locked into one course.
Assuming future tech somehow discovered a way for ships to have/get unlimited fuel/reaction mass (maybe siphoning it from an alterante dimension in-flight?), they would still do things quite differently from the way depicted in the movies.
Any ship approaching a planet or other non-accelerating object would fly (and burn) normally at first but then halfway it would turn around, point the engines forward and slow down. For an accelerating target like another ship, the goal would be to match velocities or in battle to at least slow down enough to be in range of the target for more than 1-2 seconds. That means burning retro, left, right, up, down, basically any way except forward until you're behind them.
Mounting multiple sets of engines in the various directions would just make the ship heavier and slower, so there will always be main engines in one direction, with small extras for quick and unpredictable moves.
Movies would suck
Of course, orbital maneuvers and the specifics of deep space navigation are so alien to the average movie viewer that entertainment value overrules realism even if the makers know how it should look. The feeling movies aim for is often WW2 fighter planes. bombers and battleships. Those are familiar, there's lots of action and its within easy visual range, so that's what movie spaceships look and move like.