Cecil Moore wrote:

"No waves are harmed in the process" implies that waves can
never be canceled.

No. The fact that waves do not have an effect on other waves does not
mean that their fields don't superpose.

Superposition is a mathematical as well as physical operation. You
maintain that the process of adding x to y must somehow change x and
y. You insist that superposing x and y means that x effects change to
y, and y effects change to x. But the process of superposing x and y
does not have an effect on either x or y. The only effect is we now
have the algebraic sum of x and y.

ac6xg