The first issue isn't a problem with the kobold, but more with the slayer feat. I don't have a problem with the fighter killing them every turn, but the player not really having anything to do kinda sucks.
Agreed, the feat is the problem here. I'd prefer something like 4E's Cleave, perhaps with an addendum that your attack roll must be good enough to hit the second target in order to damage it (i.e., you can't bypass a tough monster's AC by cleaving through a wussy one). From what I can see, players enjoy it more too; the chance to kill two kobolds is more exciting than the certainty of killing one.
As far as one-shotting kobolds, that's been a standard feature of the game since at least 3E. The 3E kobold had 4 hit points. A 1st-level fighter with a two-handed weapon and Strength 14+ would one-shot a kobold every time.
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