The historic aspect is the most compelling reason why the term miles is used. As stated already, before there were partner programs and class of ticket bonuses one had to fly 25,000 miles to get a free RT domestic ticket. So when someone reached that many "miles" in their account the airline as well as the passenger knew "He/She/I flew a lot of da%m miles!!!".

Socialization and language trump logic and common sense all the time. Why do I have to pay a toll to drive on this freeway? (not "free" of charges but "free" of stop lights/signs) For that matter why do we drive on a parkway and park on a driveway? (unknown credit here for some stand-up comedian)

I remember the first time I used the term "over the counter" when I was an adolescent. I was corrected by ... oh I forget.. someone ...
"That means you don't need a prescription".
Me: "That doesn't make sense. I grab the item off the shelf, take it to the cashier, pay for it, and walk out the door. It never travels "over the counter".

Really, wouldn't it make more sense to say that you can't just buy that drug because the pharmacist keeps it "over the counter". Should we try to change the English-speaking world (maybe it is just an American thing) ? No, this is how we know it. Same with miles. Trying to make language logical is futile. Why do "may be" and "might be" have VERY different meanings but "maybe" and "might be" mean the same exact thing?

The MLA gave up years ago and now "to boldly go where no man has gone before" is accepted as correct English. Forty years ago it was the quintessential example of a split infinitive.

The term "miles" was used by many foreign carriers even though they used the metric system. The term will be around for a long time.