Well, were just gonna have to agree to disagree on this one. Ash is a pokemon trainer , and as such, he has impunity to catch whatever pokemon he sees as a companion. There has never been anything established in an interview or said within the anime that labels him as "that kind of character", to not be able to have a legendary, or those that are very powerful, such as Lugia.
We've seen the series evolved to the point where Ash has caught more and more powerful pokemon to add to his current reserve roster. Ash-Greninja, Goodra, Naganadel and Melmetal is what set the bar even higher, as Ash had now been developed as a skilled enough trainer to own powerful pokemon which could rival legendaries.
I'll mention again, that this is a world tournament arc, and Ash is competing with the best trainers in the world. Trainers participating in this tournament could included trainers such as Tobias who may potentially have pokemon that are soley legendaries.
Just because Ash owns a few legendaries does not make him unstoppable or less of an underdog if he's up against pokemon trainers who have the skills to defeat possibly any pokemon. The series has shown time and again, that just because a trainer owns a powerful pokemon, does not automatically make them less of an underdog, if they aren't very skilled in pokemon battles. Iris and her Dragonite are a perfect example of this.
What reason would there be for Ash not to have a legendary, if its been showns that he's now fully capable of commanding one, having had experience owning a psedu-legendary, ultra-beast, mythical and full evolved starters. He's now reached a point in his level of understanding pokemon, that he can even use aura, trigger a bond phenomenon, and even hear their deepest thoughts (lugia).
Again, the fact that Leon is the strongest trainer there is, is all the reasoning why Ash is considered an underdog, since he still is not skilled enough to defeat him. Him having a legendary will not usurp Leon's dominance as a strong trainer, especially seeing how Ash himself has defeated trainers with legendaries, which is a feat that can be easily accomplishable for Leon or any strong trainer.
Bottom line, here is the inevitable facts, the pokemon anime is breaking trends, and Ash "WILL" eventually own a legendary sooner or later to develop his story progression. Proof of this is his ascension to becoming a champion, after competing in many league tournaments, and the other mentioned example of having powerful pokemon he's caught over the course of the series , going from possessing fully evolved starters to pseudo-legendaries & going further to owning mega-level tier pokemon (Ash-Greninja), Ultra-Beast (Naganedel) and a Mythical (Melmetal).
By story progression logic, the next further step is him possessing his own Legendary; Lugia, Ushifu, etc.