An email client is highly nontrivial, due to the complexities of the underlying standards, and how the real implementations you have to be compatible with don’t strictly follow them. Making an email client that doesn’t suck and is fully interoperable is quite an ambitious endeavor.
What complexities specifically? Implementing SMTP (from the client’s perspective) that other SMTP servers can understand is not very hard. I have done it. Does it follow every nuance of the standard? I don’t know, but it works for me. I haven’t implemented IMAP but I don’t see why it should be much harder. Is there a particular example you have in mind?
The point was to answer the question: "Can every piece of software be viewed as a permutation of software that has already been developed?" In my opinion, an email client is a more favorable example than a 3D engine. In fields where it is necessary to differentiate, improve, or innovate at the algorithmic level, where research and development play a fundamental role, it is not simply a matter of permuting software or leveraging existing software components by simply assembling them more effectively.