I mentioned melee clerics because [MENTION=67338]GMforPowergamers[/MENTION] did, and because I've had the experience personally in an AD&D game, where my melee cleric, due to superior stats, outshone the melee fighters. I'm not making any point about CoDzilla, which is an artefact of one edition of the game that I have played very little of.
I am almost always the GM.
In the event that you are curious whether, as a GM, I have encountered circumstance where rolled stats lead to overshadowing issues, the answer is "yes". Hence my preference for non-random stat generation.
The reason I use the cleric as the example (even without COdzilla) is because they still have great armor choice, good weapon choice, and if you don't self buff, just prep exploration spells and healing spells, and you can still out fight a fighter at several levels
((((To be fair 5e has made BOTH codzila less viable and straight fighter MORE then 3e did))))
it doesn't have to be a cleric though... lets take a wizard
give the wizard a crazy awesome set of rolls... and I'll go with the most crazy I ever saw 18,18,17,17,16,15... then give the fighter bad rolls (not the worst I have ever seen) 15, 13, 11, 10, 9, 7
now the wizard can go and take any race... in fact, he chooses no race... no stat bumps and no special abilities
the fighter chooses the +2 str +2 con race (I think it is a dwarf)
so we end up with
fighter 17 str, 7 dex 15 con, 10 int, 11 wis, 9 cha
wizard 16 str 17 dex 18 con 18 int 17 wis 15 cha
max 1st level hp so the fighter has 12, and the wizard has 10... the fighter where's good armor(ring mail+ shield) and has a 16 AC... the wizard casts mage armor and has 15 AC. the Wizard has a staff that attacks +4 and does 1d8+3 and the fighter has a long sword that does 1d8+3
the fighter once per short rest may take a second action (action surge) and the wizard has spells...
how much worse would it be if the wizard was the fighter's brother, and the same type of dwarf...
wizard 18 str 17 dex 20 con 18 int 17 wis 15 cha
with 2 more hp they have equal hp, and the extra +1 to hit and damage is insult to injury...