The new saws have tri-angle teeth. Each little tooth has three different angles, plus, the steel is high carbon and very hard. The abarsion needed to sharpen an edge, can heat the metal and change the original hardness.
In the old days, yes, it was economical to sharpen the saw.
To tell if it's a tri-angle tooth, just look closely at the tip of the tooth. To tell if it's a high carbon steel saw, just try to file it, hehe.