Good Nicholson files run around $12 each. A gallon of acid will keep them sharp forever. Replacing them if you use them a lot gets damned expensive. So does buying cheap ones since you then do a lot of replacing.
You might get one or two "sharpenings" out of a chemical bath on a file before the teeth are dissolved enough to not make a difference. I've tried it a few times, not worth the effort for what little gain it makes. If files cost $50-$100 like some carbide endmills, and the "sharpening" actually got them like new again, then it would be worth doing.
If I spend more than 10 minutes horsing around trying to sharpen an old file, I'm losing money. I am money ahead to buy a new one and toss the old one in the garbage.
Its the cost of doing business. Properly budgeting consumable tooling is part of operating profitably. Time not spent making shop rate is overhead, and I would rather myself or my employees make money instead of wasting it attempting to sharpen a $12 file.
If you're in your home shop and you have more time than money, you may find it worth it. But I value my time more than that, so I'll just replace my files when they get dull.
I used to work for a guy in an auto body shop who would spend 5 minutes of time at $60/hr and a dollar's worth of lacquer thinner to wash out and save the paint mixing cup that the paint supply would sell for .50 cents. Talk about tripping over dollars to save nickels. That job taught me a LOT about balancing time vs expenses.