-A slayer, at first level can autokill any commoner he dislike
-A slayer, at first level, can autokill a bird flying at a distance of 319 feet. Blindfolded.
-A slayer, at first level, can damage an ancient dragon. Or a God. Maybe only a bit. But he damages it.
You shouldn't kill on a miss.
Why is this a problem for a fighter, but not for a wizard? The wizard can do automatic damage at 100' range, and on average more than the slayer's 3 points in melee or piddly 1 point at range.
-A wizard, at first level can autokill any commoner he dislike from 100 feet away, and can do it every 6 seconds all day long
-A wizard, at first level, can autokill a bird flying at a distance of 100 feet. He can do it while prone and aiming through a hole in a wall the size of a golf ball, as long as he can see the bird.
-A wizard, at first level, can damage an ancient dragon. Or a God. Maybe only a bit. But he damages it.
Dealing damage is supposed to be the fighter's strong suit, if the wizard is more reliable and safer damage at first level and increases in power faster like wizards traditionally have, then when will the fighter get to shine? At level 3, the fighter is still doing their 1 or 3 on a miss, the wizard is now doing 2-5 to two targets, or 4-10 to a single target. 4-10 damage automatically from 100' away sounds nice compared to 7-14 damage on a hit, 1 on a miss, every other round (unless you want disadvantage) that the fighter has at range, or 10-20, 3 on a miss while taking melee attacks. The wizard just keeps getting better too, doing an automatic 6-15 at 6th and 8-20 at 9th.
Saying "because it's magic" doesn't cut it with me. Flexibility is the wizard's strength, raw damage dealing ability is the fighter's. If you don't think it is realistic, try fighting in melee with someone who is combat trained, can deadlift 800lbs, and is wielding a 20lb axe, and let me know if you can avoid them doing some sort of damage to you every 6 seconds if they are really trying. Even if they miss, the axe hitting the wall or furniture near you with that much force behind it is going to generate some significant shrapnel. I can see removing Reaper from ranged attacks, but being in melee with a slayer should be a very painful experience.
As a side note, I will be shocked if ancient dragons and gods don't have some way to completely ignore the couple points of damage on a miss. Worst case all they need to do is take a good strong drink before the fight, being intoxicated guarantees that they will ignore the 1 point at range and gives them a 66% chance to ignore the 3 points in melee.