Thank you for posting, but I have to disagree with taking license to redefine an entire field of engineering:
> …I would like to define systems engineering as “analyzing different aspects of a system in order to better understand the performance or correctness characteristics”
Here is a much better definition of systems engineering from which to make your argument:
“Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles.”
Wikipedia
Personally, I would add “specify” in addition to design, integrate, etc. based on my 30+ years of systems engineering.