OK, here they are, filthy adult only pictures.
My test file is an old favourite. I bought it government surplus the first time I needed a file, so it's at least 40 years old. Made in India, it contradicts conventional wisdom that Far Eastern tools are all rubbish. It's been abused – only since retiring have I learned to respect files. Most recently the file was used to take burrs off lathe turned edges.
First, the file before treatment. It's dirty and blunt. You can see brass, aluminium and steel chips.

I made a 20% by volume solution of Sulphuric Acid Drain Unblocker. This appears to be mostly concentrated sulphuric acid with additives. Although the acid isn't quite strong enough to char paper, don't splash it around. Always dilute by adding the acid to a large surplus of cold water, never the other way round. (The water gets hot; overdo the acid and the mixture will boil, spit or even go pop. A face full of hot drain cleaner will ruin your day.)
Next the same file after a good brush with a file card. You can see that the edges are dinged and that the ridge tops have a shiny polish.

This is what an almost new file looks like. The edges are in much better condition, and nothing shines!

This is the file after 30 minutes in the acid. Despite vigorous bubbling, the improvement isn't all that obvious. Out of the acid the file is covered in a black deposit (Carbon?) and has a strong unpleasant 'metal attacked by acid' smell. The photo was taken after rinsing the file under a tap and going over it with a tooth brush.

After 14 hours in the acid it's black, with small white crystals, and lots of dark grey particles. Yuk!

After another rinse clean. Now the ridges are a bit sharper. The shiny polish on the ridge tops has gone. Not perfect by a long way, but certainly much better than Photo 2. It's easier to feel the difference than to see it. Try rubbing the file with a finger before and after.

Top down photos make the file look flatter than it actually is. Next is the best I could do to capture the tooth profile. Bit rough, but it has lots of sharp edges.

I've tried acid sharpening with number of old files. This example is neither good nor bad. Some treated files last quite well after sharpening, others don't. Looking at the pictures above you can see signs of pitting. I guess this would tend to reduce the local strength of the teeth, perhaps causing them to wear more quickly than a new file would.
Andrew mentioned in his Original Post that he used Phosphoric Acid. This has a different reaction to dilute Sulphuric Acid. Sulphuric reacts with both Iron and Iron Oxide. After removing the rust it dissolves metal as well. Phosphoric Acid reacts with the rust to form an corrosion resistant layer on top of the steel. I don't think the phosphate layer is hard, so using the file probably removes it quickly. I'd guess that Phosphoric Acid is best for recovering a sharp file that's gone rusty, and Sulphuric is best for recovering a blunt file.
Of course we may be seeing another effect as well. Simply giving a clogged file a good clean sometimes works wonders.
Dave