Can a serrated bread knife actually be sharpened, or is it a disposable item people are embarrassed to admit they replace?

The flat-side step above is the whole game and worth expanding, because it is where people go wrong in a way that convinces them the method does not work.

When you work the scallops you push metal to the other side. That burr is thin and it will cut nicely for one loaf and then fold over and be worse than when you started. If your experience of "I tried sharpening a serrated knife once and ruined it" is that pattern, this is what happened.

Deburring is a light touch on a fine stone with the blade absolutely flat, or a few passes on a strop, or even drawing it through a piece of end-grain wood or cork. Almost no pressure. You are removing something the thickness of a hair.

One diagnostic before you start, since you say it tears rather than fails to cut: look at the points, not the scallops. On a bread knife the points are what break the crust, and they blunt long before the curves inside do. Hold it up to a light and look along the tips — rounded, shiny flats where there should be points is the usual finding on a knife that tears crust. That tells you the tips need the most attention, and it also tells you the knife is not worn out.

And never run a serrated knife through a pull-through sharpener. That is the one thing that genuinely destroys them.

They absolutely can be sharpened, the "cannot" line is wrong, and the reason it persists is that the method is unlike anything you do on a stone.

Start by understanding the geometry, because it makes everything else obvious. A serrated edge is bevelled on one side only. The other side is flat. Each scallop is a tiny curved edge, and the points between them are what actually start the cut.

So the work is:

One scallop at a time, on the bevelled side only. You need something round that fits inside the scallop — a tapered sharpening rod is the purpose-made tool, but a round or half-round needle file, a chopstick wrapped in wet-and-dry paper, or a ceramic rod all work. The taper matters because your scallops are not all the same size; you slide the rod in until it seats and use that spot.

Match the existing angle, do not invent one. The bevel is already ground and you are refreshing it, not reshaping.

A few strokes each, all in one direction, working along the blade. You are raising a small burr on the flat side.

Then lay the flat side dead flat on a fine stone and take the burr off with two or three very light passes. Flat means flat — no angle at all. This is the step people miss, and skipping it is why a home-sharpened serrated knife often cuts worse afterwards.

Twenty minutes for a bread knife, and it will be a different knife.

The honest economics, since you asked whether it is a consumable.

A serrated edge lasts a very long time compared to a straight one, because most of the cutting is done by the points and there is far more edge length in the same blade. A bread knife that has gone dull has usually had years of use, not months. So it is not a consumable in the sense of a razor.

Where the disposable framing comes from is the bottom of the market: a knife with a stamped, very thin serration and a hardness that will not hold an edge is not worth twenty minutes of anyone's time, and there are a lot of those. If yours is a decent knife with well-formed scallops, sharpening it is clearly the right call.

One genuine limit to know about: some serrations are ground so shallow that there is not much bevel left to work with, and some knives are bevelled on the side you would not expect. Look at yours in good light before you start and work out which side is flat. Two minutes of looking prevents the one mistake that is hard to undo — working the flat side, which rounds the points off and does turn the knife into a bin item.