I believe that the urge to say “yenna machla” actually stems from a good place.
The Gemara often uses euphemisms to avoid describing things that are deemed too explicit or shocking. Probably, the origin of “yenna machla” was not a superstitious ritual to prevent bringing cancer upon oneself, but rather an attempt to euphemistically minimize the shock value of the word.
Unfortunately, what the term mostly succeeds in doing, nowadays, is further stigmatizing an already stigmatized condition within the Jewish world. Cancer is hardly a rare and unspeakable condition nowadays, and to use “yenna machla” to describe all forms of it lumps the treatable in with the terminal and the survivors in with the deceased.