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.