In fact many of these things are possible once you realize magic items don’t have to be magic items. I can think of a few scenarios off the top of my head.
First, perhaps everyone DOES get it, but at a cost, the cost being the price of a +1 weapon, which must be paid in order to hire 1 on 1 attention from an ancient fighting master who can teach you his ways. One month or more of study may be necessary, in fact the time spent “crafting” it may require not only the master, but the student.
This leads to all sorts of potential madness, such as a fighting type performing “spell research” to discover new fighting styles, which he then teaches to others who seek him out.
But if all that’s a little bit too out there, you could simply do something like giving whatever benefit you’ve concocted to the person who scored the killing blow, or to whoever built enough of a rapport with the grouchy martials arts master who is only willing to teach one student (and learning it is much different from being enough of a master to teach it).
4e also did “inherent bonuses” for dark*sun, so it’s certainly not unheard of. I think the reason you don’t see it much in old school is twofold: 1) nobody thought of it yet and 2) the +s weren’t essential to the math of being able to hit things yet.
You should be able to do low magic and then life is just difficult but feasible for old-school PCs. However if you know your PCs will be sad if they don’t get a carrot every once in a while but you want the FEEL of low-magic, you could use some substitutions like the ones proposed above.