Surprisingly, with PNG, the deflate compression can slow you down, depending on what you are doing with the data. Saving a little bit of IO when you're accessing local data can turn out to be a losing proposition. TGA makes it easier to just shove pixels around, from program to program. TGA has all sorts of weird options which you can ignore, but with PNG, compression is mandatory.
JPEG is a file format from decades ago. Obviously it’s possible to do better today. But it’s not possible to just invent a new format and have it as widely usable as JPEG. PNG did this with GIF but really only because GIF was seriously hobbled by software patents. It’s doubtful the millions of colors and alpha transparency would have won over compatibility otherwise.