Why are the ileum, cecum, and ileocecal valve removed with appenditis?

Generally they are not removed during an appendectomy. But before the pathology of appendicitis was discovered, advanced cases of infection led to inflammation of the adjacent cecum and ileocecal valve. The terms typhlitis and typhlodicliditus are rarely used nowadays. They were almost always accompanied by perforation and fatal peritonitis in the pre-antibiotic era and the condition was diagnosed at autopsy.

Possibly these organs were found to be involved in a rare case, so they were removed. Rarely a carcinoid tumor is discovered in the appendix, and the surgeon chose to do a more extensive resection. I'm just guessing here.

Because they aren't. You seem to have gotten some bad information someplace.

So the other organs don't attack them.