On any chain-driven device, as the chain stretches, it begins to wear away the teeth on the sprockets. Essentially, this is caused by the stretched chain widening the space between the teeth. Typically, the teeth begin to "hook over" as the chain rides higher upon the teeth due to its inability to fall down into the lower area between the teeth which transmits the drive forces into a higher position on the teeth side-walls. - This is because as the chain stretches, the distance between the link pins on the chain has increased and this precise fit into the teeth is no longer there. (Typically the chain is of a higher strength material than the sprockets. Escially when you are speaking about the front chain-rings which are typically aluminum, making the softer material of the front rings wear more rapidly than the steel rear freewheel cogs)
When you place a new chain onto worn and elongated teeth, you often have a "skipping" of the chain, (especially under load on smaller diameter cogs as the chain is in a tighter arc as it passes around the cog and is in contact with a fewer number of teeth when under load). This is caused by the new chain as it protests being forced into teeth openings that are not a match for the dimensions of the new chain. This usually manifests itself on high-miles bicycles on the cogs that had been used the most. (On a 1972 Schwinn Sports Tourer I worked-on recently, a new chain had been installed and there was an under-load skipping of the fourth gear rear cog. I deduced that this was the cog the user had preferred for most of his riding and therefore had the most wear. As those teeth were worn just enough to cause this, there was no other option but to replace the freewheel.)
So, sharpening the teeth will not typically make any difference as the center to center distance is no longer within original design specifications, and removal of more material only shortens the life of the already worn components. Replacing the chain will also shorten the life of the worn sprockets as they will wear in reverse as they try to fit back into the correct chain-pin spacing, taking away even more material from the teeth. On high miles applications, the only true solution is to replace chain and all sprockets at the same time so as to return everything to original design specifications.