Exactly. Take a look at almost every class feature the Fighter gets as they level. In the earliest version of the game... you'd only get those mechanical features through acquiring magic items, not from receiving them as part of leveling up.
This is why even 5E doesn't give you a true "old school" feel... because of the all mechanics you get at each level of the game. A +1 sword will never feel important because your attack and damage bonuses are already pretty high just based on the new modifier chart, Fighting Styles, raising your ASIs, your proficiency mod going up, extended crit ranges, bonus superiority dice etc. etc. etc. That extra +1 from the sword is barely anything in the large swimming pool of bonuses you already have.
To have a real OSR experience... you need a Fighter who has like a +1 to hit, a +2 to damage, and
that's it. That's the extent of their combat mechanics until they start finding magic items that let them do all the other stuff.