AD&D/D&D has always promoted PCs as being slightly special, better than the ordinary people around them. There used to be the classic 'Level 0 commoner' who made up the bulk of the world's population. That is what you would be if you were a farm-boy just deciding to leave the fields and become an adventurer. Just like a Level 1 Wizard is not an apprentice but a fully-fledged mage, a Level 1 Fighter is presumed to have some experience of combat. That's why D&D5 uses Proficiencies - they represent your training or past experience. Older editions had class abilities which reflected a similar previous experience.
Improving Stats by level is a recent thing, brought in from 3e. Whilst there were magical ways to improve your stats in previous editions (and optional rules on training them up), you were generally stuck with whatever you rolled at the start of character creation. This led to odd situations where a Level 1 Fighter could be a better warrior than a Level 3 Fighter thanks to the bonuses from very high stats..
