Another, non-game example of where weapons tech can take you, is Perry Rhoadan. german science fiction started in the 60s. Perry Rhoadan becomes immortal and leads humanity, and for periods the whole galaxy, for thousands of years. There you see actual technological progress, often stolen from other races. It leads to a point where a deus ex was used by authors to reign it back in (hyperspace resistance increased rendering everything too advanced useless). Point is, at the height of it, single shot starship weapons had aroud 2,000 GT TNT equivalent of energy, ships carried a lot of them which had and could be aimed at almost light speed to single point (in the physical sense as they had multilayered shields that could only be penetrated by point-fire, every "point" of the shiled had the same strength). i only wondered how ground combat would look like, as the battle armor and robots carried the same tech. I would assume a city would be reduced to sub-atomar dust within the first 10 minutes of an engangement or so.
but from a technical point of view it made sense, same for power generation and computers (even if computers also got the actual processing power development wrong). Nice thing, they used real world ISO units for the most part, not like start trek which just throwns around units to sound scientific.
Some ship examples: Accelaration: up to 980 km/sec^2, overlight factor up to 60 million, energy directly from hyperspace. So you can see why that, from an authors perspective, had to be rained in. when travel to the next couple of galaxies can be done in a private yacht, things get a little bit to crazy.
EDIT: Typos, a lot... Sorry for that!
They miss, and they miss a lot. Firefights in Star Trek look mostly like firefights everywhere else - beams and bolts flying through the air, and every now and then someone gets hit.
One interesting aspect is that TNG-era phasers used by protagonists don't even look like practical weapons. I read somewhere that this was intentional design decision - Starfleet was supposed to be about peace and exploration, so they didn't want the protagonists carrying something recognizable as a gun. Star Trek back-tracked a bit from that later on, with introduction of phaser rifles that look not unlike something you could really see on a battlefield of the future. But back to the TNG phasers - because they're shaped more like a flat flashlight than a gun, they really must be tough to aim. I mean, try taking a laser pointer and hitting something a couple meters away from you with the first click of the button. It's hard. In my headcanon, phasers must run some sophisticated auto-targeting systems - otherwise, the feats of accuracy seen on the screen would be impossible.
Source: Star Trek Design, by Judith & Garfield Reeves-Stevens
But if I keep thinking in-universe style, the Star Trek / Federation culture on surveillance could have come from some hard won failures earlier on.
The future would likely include lasers as some kind of a weapon, which indicates to me that engagement ranges would be so massive that even light will have a significant amount of travel time.
Ok at that point the avionics fit for a fire team would buy a small starship.