It wasn't a "failed pilot" or there would never have been a second pilot. It was borderline at worst. And of course it's part of TOS.
Not to most people. Most have no clue there is anything before Kirk shows up as Captain, You think some writer at EW would know what the cage was? I am many others do not include the cage when I/we say TOS, as its not part of the TOS. Its what the show would have been if it had been approved as is.