A. Fighters were the toughest class, and that mattered.
Hit points ... I mean, they matter in 5e, but not that much. In 1e, they really mattered. And fighters got all the hit points. To start with, fighters got d10 hit points. They were the only class to get d10. Clerics? d8. Thieves? d6. Magic users and monks? d4.
Except when the rubber met the road that didn't matter much. Clerics had almost as many hit points, had as much armour, and could heal. Unless it was a one shot situation or L1 the Cleric was tougher.
See, 1e also provided for constitution bonuses to hit points. All classes could get +1 or +2 to hit points/level (for scores of 15 or 16 in Constitution). But only a fighter could take advantage of a 17 or 18 in constitution to increase that bonus to +3 or +4, respectively.
Or slightly less than 2% of fighters could close the gap on clerics a bit
B. Fighters were the strongest class, and that mattered.
For characters who did not roll three sixes no they didn't. For half of all the remaining characters that were rolled fairly they barely did (+0 to hit, +1 damage for 18/49 Vs just 18)
With honest rolls this almost never mattered.
C. Fighters were the only class that could use any armor, shield, and weapon.
Fighters only real advantage over clerics was, when push came to shove, the fact the rules (with bonus damage Vs large creatures) and especially the magic items tables were weighted towards swords.
Interesting how the third worst 1e class shared that with the second worst class - the thief. (The worst was of course the 1e monk).
D. Fighters were the only class with multiple attacks.
...
First, fighters get 3 melee attacks per two rounds (one attack in the first round, two attacks the second round, repeat) starting at level 7, and then two attacks a round starting at level 13. Which is good!
So that's an actual lead at level 7. And a bigger one way after the level soft cap
Gygax himself came to realise that 1e fighters were just plain bad and Rob Kuntz being able to run rings round him with Robilar screwed up his playtesting. As he was explicit about on these boards that was why he added weapon specialisation - for game balance. And if Gygax said it was for balance I trust his judgement more than yours on this.
The long and the short of it is the best a 1e fighter could hope for was to become a bard.