What is a system? It would depend entirely on your use of the word 'system'. A quick look at a standard dictionary entry will reveal that the term can be applied in different ways.
Removing something from a system may or may not render it useless. A cog from a clock would likely render it useless, whereas removing the planet Neptune from the solar system would not result in the Solar System no longer existing.
Words can have mulitple meanings and used in an infinite number of sentences.
Abstractions are abstractions. How and why you apply them is up to you. The uses of doing so have limitations.
Perhaps an interesting argument but, surely, a valid definition of a system must answer the question that is implied by your argument, not so? — Pieter R van Wyk
Not so. The manner in which we use language need not be rational. If anything it helps to either obscure or highlight irrational thoughts and deal with (or not).
A valid definition has nothing much to do with a valid argument.
P1: Potatoes only Eat People.
P2: A Potato has Eaten.
C: A Person has been Eaten.
How I am defining Potato/Potatoes, Person/People and Eat/Eaten is irrelevant.
If the term 'system' can be used in various ways for abstract and physical systems. What you are trying to ask for is something like the height of a human being. There is no definite answer to this, only a set of limits. Which is, ironically, probably a valid definition of what a system necessarily is. Such a definition also deals with the Set of All Sets, as this could not be a definition according to what I have just said as it has not limits.