I have a problem with the ability that let's him do it without an attack roll. I have a problem with him being able to slaughter 95% of all humanoids WITHOUT A ROLL, every attack all day long.
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Example? Okay. Fighter goes into a bar. In that bar there are.. 20 villagers (level 1/0 basic level Joes just having a good time). The fighter pulls out his two handed weapon (though he could be snapping his fingers - as his strength bonus does all the work) and proceeds to slaughter everyone in the bar with zero effort. He does this without needing to roll a single attack roll. He does this by being with melee with them for a single "attack". He does this as long as he is in melee with them no matter how fast they are (DEX score, ability to dodge), how much armor they are wearing (increasing their AC), he does this without needing to make a SINGLE attack roll.
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There are differences I'll grant, but the fighter has snowflake status that none of the others do. He doesn't need to roll. He doesn't need to worry what the other people can do, what they are wearing, where they are. He can effectively battle blind, or snap his fingers (as his STR is doing the work) and kill people. He can snap his fingers because his weapon is irrelevant - he kills the 3 hp people with a 0 roll on his weapon's damage dice. He breaks the game, in character and out of character, in ways that others can't.
(emphases added)
If I count correctly, you make variations on the same claim nine times: the fighter's player doesn't need to roll to hit (5 times), or can somehow roll a zero on damage dice (once), and, within the dramatic world, could be "snapping his fingers" (twice) "with zero effort" (once).
Each of these claims is false (mistaken, as I see it) based on what is stated in the rules of the testpack.
* In order to "miss", the fighter's player does need to make an attack roll (and so be in combat and choosing to make an attack roll as her action) -- How to play, p. 19 "Attack basics".
* damage dice are only rolled on a hit, and zero is not a result that ever arises -- How to play, p. 20 "damage rolls"
* to gain the benefit described as a first-level character (others can get it at higher levels), the character needs to be a fighter who has chosen one of five fighting styles (Classes, p. 25), and the character needs to "miss a target with a melee weapon which you are wielding with two hands". There are therefore a number of conditions that need to be met, and snapping fingers , even one handed, would mean that they are not being met.
* indeed the rules do describe circumstances which are "so easy, so free of stress or conflict...that there should be no chance of failure" (DM Guidelines, p. 1) in which rolls are not needed -- which may be taken to include your "zero effort". Since a melee attack roll is needed, this by definition isn't one of those circumstances, and the specific rule provides a unique case in which the "chance of failure" to roll a weapon's damage die, modified, etc., does damage to the target in any case.
* snapping isn't "improvising an action" either: a DM may allow you to snap fingers while wielding a two-handed weapon, etc. (How to play, p. 19), but the damage will be done by the attack.
* I get that people's understanding of what hit points represent varies, so again, let's read what's been given to us (How to play, p. 22): "Hit points represent a combination of physical and mental durability, the will to live, and luck. Hit points are an abstraction..." Of the four things here, only one of them (physical durability) pertains to the circumstances you describe, as I see it, leaving the other three that could be represented by the damage that is being done to your hypothetical villagers.
Repeating the same unsubstantiated claims over and over is not persuasive. You are correct that the situation you describe is ridiculous. Fortunately, that situation is not related to the rule being discussed. If you read the rules differently, then please spell it out.