Hi achrn. I was almost convinced by your logic until I looked in the Concise Oxford Dictionary of English Etymology, where "Near" (adv) is defined as almost, nearly! On this basis, near is synonymous with nearly. Therefore my opinion was consistent with this definition.
I then looked in the Shorter Oxford English Dictionary itself. There are a lot of different definitions depending on the context. I did find " Denoting approximation in degree or amount', (which is accordance with your point 'a miss that was near') defined as "within a (very) little, almost (Now usually expressed by Nearly!). Again indicating near is synonymous with nearly.
In Roget's Thesaurus, Nearly means practically, almost, all but, more or less, near enough, roughly around, in the region of, about, approximately, thereabouts, as good as, within an ace of. The latter is about as close to the intent of the term near-miss as you can get: within an ace of being hurt, etc.
Interestingly, the term near-miss is not in either of the Oxford English texts. In Rogets Thesaurus 'Close call' comes under escape, avoidance, i.e. narrow escape, hairbreadth, close shave, close call, narrow squeak, near thing. Again no 'near-miss". or its opposite 'Near-hit'.
So, now we have explored the English Language a little, this series of posts has made my point. The term 'near-miss' means different things to different people and causes confusion. There are better terms such as 'Close-Call, or even better 'Potential Incident'.
Thanks for the fun.