But, all that being said, in 5e, there IS a ninja class. It's the Way of Shadow monk. It's right there in the description of the class. Now, it's not the same as a 1e ninja, that's true. It's a new interpretation for a new edition. IIRC, the 3e ninja was closer to a rogue than a monk (but, it's been a really long time and I might be misremembering). But, at the end of the day, there is a ninja class in 5e. And, it's a ninja class that does ninja things most of the time - illusions for distracting, disappearing into the darkness, kicking butt out of the darkness. Yup, that's a ninja. It's not a 1e version of the ninja, but, it is a ninja. It's just as much of a ninja as a barbarian is a barbarian or a bard is a bard.
To preface what I am about to say, I am for Warlord inclusion. I am on your side, I just find this particular argument completely ridiculous. Have you read the PDK description in SCAG? It says pretty much exactly the same thing as Shadow Monk does about ninja.
"Banneret serves as the generic name for this archetype if you use it in other campaign settings or to model Warlords other than Purple Dragon Knights."
in comparison to
"These monks might be called Ninjas".
To paraphrase you, it might not be the warlord you want, but it is right there, with the label on it and everything. How can you use this argument of Shadow Monk being the Ninja (Just not the ninja a ninja fan wants), but feel fine with refusing the PDK that meets exactly the same criteria you are saying makes the Shadow monk a Ninja?