> Writing isn't an engineering discipline. And all industries rely heavily on writing. Could it be that writing software is just writing for computers and as such could only by codified within another engineering discipline and not by its own?

I think this is a very good point!

If you are writing the control software for a rocketship's avionics, you probably need to have some understanding of aeronautics, control theory, signal processing etc. Ultimately the act of writing the software is merely an expression of all the math and theory that you have spent a lifetime acquiring.

Inversely, the engineer who is speccing out the control software for a nuclear reactor is essentially writing the software for it. It's just in human readable format such that the human journeyman who's actually slinging the code can implement it. By the time the code is being written, the engineering work has been done already.

Programming is much closer to bricklaying or assembling or machining. Software engineering is much closer to architecture design, and does not involve a lot of code writing.