Embedding a terminal in a file manager solves a particular problem. It synchronizes the working directory of the terminal with the directory open in the file explorer. This is a pretty common problem to have, and there certainly are other solutions to it, but embedding a terminal within the explorer is a good solution for a lot of use cases. It's convenient, and it makes sense for a program that manages your files to enable you to more directly manage files with a terminal prompt.
It doesn't really make sense for a file manager to embed an email client because email doesn't usually involve file management. Needing to send an email from a particular directory isn't a problem that anybody has.
Could you synchronize a terminal window and a file explorer window? I'm sure you could with a bit of effort. You could also set up a whole tile manager and dock those two windows together.
For people who don't want to do all that, or don't use or don't like tiling, or who just want to run chmod +x on the file they downloaded, putting a terminal in the file manager is a perfectly valid solution to a relatively minor inconvenience. It even has a hotkey to close it when you don't want your window spoiled by a horrible subframe.