To-hit rolls are an RPG mechanic inherited from pen-and-paper systems. They represent an obvious intuition (attacks can miss) and use a binomial mechanic with a random chance. Many non-RPG computer games use a different mechanic: did the sword, shot, spell, or whatever hit the target?
One of the City of Heroes developers remarked that, had he to do it over again, he would not have included a to-hit roll or an accuracy stat. Every attack would hit unless some defense caused it to miss, and then you would have an indicator of why you missed.
The relative merits of damage mitigation versus avoidance are a rich topic, not to be explored here. One note is that the difference really matters when there are secondary effects. If an attack does X damage and blinds you for Y seconds, a miss means neither X nor Y, while a mitigated attack means taking X/z damage and the full blind. You could also have mitigation apply to the blinding, but that is usually handled through another mechanic, such as resistance to burning or quicker debuff recovery.
Accuracy stats facilitate high variance effects. For example, an attack that does 100 damage with 100% accuracy has the same DPS as an attack that does 1000 damage with 10% accuracy. The difference is consistency and the importance of damage spikes. Against a target with 90 hit points, you prefer the reliable attack. Against a target with 100,000 hit points, you are relatively indifferent. Against a target with 500 hit points and 200 points of damage reduction (or that regenerates 100 hit points between your attacks), you prefer the inaccurate attack. (There is a similar spike effect with fast, weak attacks and slow, strong attacks.)
Accuracy rolls are seen in many games, sometimes surprisingly so. First person shooters, for example, often include an accuracy mechanic. Bullets do not necessarily go where your gun points. Sniper rifles usually have pinpoint accuracy while shotguns shoot a cone in a general direction. This is often handled invisibly. Borderlands attaches a specific accuracy stat to each weapon and then accuracy bonuses to characters and abilities; the Mechromancer has many abilities tied to lowering accuracy, and I am not sure that I know what -500% accuracy would mean. (Note: this is not exactly the same mechanic, because it moves the bullet in a semi-random trajectory around the intended target, as opposed to having the bullet reach the target and then give it a chance not to hit anyway. I recall having seen games stack “accuracy” systems where you need both to aim properly and to pass a roll, but examples are not leaping to mind.)
NPCs in FPSes need an accuracy stat because the computer’s default is perfect accuracy. (“I flinch at each shot, because I understand now that every bullet fired is ending a human life. Otherwise SAP wouldn’t have pulled the trigger.” Robopocalypse by Daniel Wilson) If you want to see how that changes the game, see the Scarecrow in Arkham Asylum or Deadshot in Arkham City, both of whom instantly defeat you if you enter their field of vision.
In Dungeons and Dragons, armor classically reduces the chance that you are hit rather than reducing damage; either you hit for full damage or you miss, and damage reduction abilities were added in different forms in different editions. Also classically you have a 5% chance for a lucky hit (and/or critical) and a 5% chance for an unlucky miss (and/or fumble) no matter what. City of Heroes and many D&D-based games kept the auto-hit/miss rolls, down to the 5% chance of each.
City of Heroes added pop-up text to the pop-up damage numbers indicating when defensive abilities mattered. “402 327 Deflect! 239 Deflect! Deflect!” I think demand for Force Field/* Defenders shot up dramatically after that. The Lord of the Rings Online did something similar with block, parry, and evade, and then partial versions of each.
Guild Wars 2 implemented the CoX vision: every attack hit unless it had a reason to miss. There was no inherent miss chance. You could miss by being too far away or because your projectile did not hit the target (obstructed view, darting movement). You could force a miss with the blind condition, the aegis boon, by blocking, or by dodging (some abilities have an equivalent “evade” effect). Indicators of why the misses happened were spotty; you saw messages for blocking, evasion, or obstruction, but a simple “miss” could come from several effects
Some games that do not use accuracy have a few units (or an entire race) with miss chances. Doing so highlights the unreliability of the units in question, and the “miss” chance might be something else entirely: an experimental explosive that is a dud, a race distracted by shiny objects, or some technobabble about quantum mechanics meaning that the attack does not work 50% of the time. If everyone has 90% accuracy, a 30% miss chance does not sound that bad, but when the default is always hitting, any miss chance feels meaningful.
As a player, reliability is usually on your side. Unless a huge damage spike is all that matters, randomness hurts you. This is basic game theory. In an average fight, you win with most of your health and then need a few moments to recover. If your luck is very good, you will kill the monster in fewer attacks, shaving some seconds off the fight and recovery. If your luck is very bad, you die. The monster has the better upside. Refer to the math above: if the monster has 500 hit points, a 100% chance/100 damage attack always wins in 5 attacks, while a 10% chance/1000 damage attack unfavorably combines unreliability with overkill.
On the other hand, players seem to really like overkill and big numbers, and an unlikely string of misses is a chance to complain on the forums.