What is the purpose of "proof" vs. alcohol by volume?

I don’t drink alcoholic beverages often and so I am puzzled by the purpose of having “proof” vs. alcohol-by-volume. Seems that all the information you could get out of “100 proof” is already provided by the ABV (50%; ) if anything, it seems that “proof” causes unnecessary confusion (someone could easily mistakenly think that “35 proof” means “35% alcohol by volume”.)
Is it a matter of tradition/convention?

Yes. Tradition runs rampant in the booze biz. Per wiki: The term “proof” dates back to 16th century England, when spirits were taxed at different rates depending on their alcohol content. Spirits were tested by soaking a pellet of gunpowder in them. If the gunpowder could still burn, the spirits were rated above proof and taxed at a higher rate.[1] Gunpowder would not burn in rum that contained less than 57.15% ABV. Therefore, rum that contained this percentage of alcohol was defined to have “100° (one hundred degrees) proof”.[2] The gunpowder test was officially replaced by a specific-gravity test in 1816.[1]

Most alcohol bottles these days list % ABV in addition/instead of proof.

The original definition was ~1.75 x ABV, which is less clear. It was invented by the British who were still enamored with their 240 pence to the pound system and wanted to make things difficult.

In the modern era, yes because of tradition, because proof is “classier” than ABV.