I know in many circumstances white takes on c6 when they want to play e5 as it removes the defender of the e5 square. (In some other instances it may be to open up the d-file with tempo. Another reason could be to free up the queen from defending the d4 knight.)
Tbh I don't know if I understand it fully in all cases but these are some good reasons to take on c6 that I have seen. The main one being the removal of the defender of e5.
I already know many of the lines where White plays Nxc6, so I'm not looking for just book/engine lines, I'm trying to get a more conceptual understanding of when that specific trade should be played and why, as well as if/when White should decline and move the knight back to, say, b3. I most often see the Dragon so that's what I'm most interested in, for example the following:
So in positions proceeding from here (and/or similar ones) what are some features I should keep in mind to spot when that exchange would be beneficial on my own?