The answer to your question is pretty boring, it basically boils down to "because it took them that long to be recognized", but the previous "ruler" of Mexico-Tenochtitlan is his founder Tenoch.

So lets back up a little bit to the beginning of the 14th century, the Mexicas are one of the if not the very last groups to arrive into the Valley of Mexico, from Chapultepec and settle into Mexicalzingo, they spend some years working as... err... mercenaries I guess you would call it for the cities of Culhuacan and Azcapotzalco, 2 of the if not the most powerful cities in the region at the time, eventually they get recognized by the tlatoani of Culhuacan who gifts them a princess to marry, at which point they commit something of a diplomatic faux pass, they skin the princess and wear it as an offering to the "new" Altepetl they are founding with the recognition of Culhuacan, the king of Culhuacan is unsurprisingly, slightly annoyed about the whole thing about it all and declares a war of extermination on the Mexica... whoops.

Now at this point let me make a little detour, so, the Mexica as I said are one of the most late arrivals into the Valley and are not particularly in tune with the rest of the nahuatl or their customs, wont be for a while yet, so while to them this was an honor (a mistake they wont ever repeat to my knowledge), to the rest of the Valley it was a very grave crime.

Now, why the princess? well, by this moment the cities in the Valley of Mexico have elevated the Toltecs -a civilization that might or might have not existed- to a place of honor, with much of their culture and customs (some works even say that the language), descending from this semi-mythical previous culture that just happened to go away... somewhere by the time the Mexicas reach the Valley of Mexico, as such, the blood of the Toltecs that most of the rulers in the Valley of Mexico have flowing through their veins at this point gives a certain degree of Prestige, a prestige the Mexica, being new and without Toltec blood lacked, something they had hoped to remedy by marrying one of Culhuacan's princess and then screw up, this also means the Mexica at this point are not recognized as a "people" by the rest of the Valley, but as Chichimecs (ie. they dont have an Altepetl, a city of their own).

Now I've never seen anything suggesting the ruler of an Altepetl had to be of Toltec blood, and in fact Mexica society was meritocratic, the "pippiltlin" title could be obtained by anyone, and their form of government was a form of indirect elective democrat-ish monarchy, with polities like Tlaxcala for example outright being ruled by a Senate, still, prestige, is prestige which the Mexica lacked.

Okay, so Culhuacan stars a war with the Mexica and drives some of them (though Mexicalzingo itself will go on), out of the Mexicalzingo, and into Tlalcan swamp, were they will go on to find an eagle devouring a snake on top of a nopal (or in a white island bleached by bones, or on top of a white nopal, or the snake was white, accounts vary) and build Mexico-Tenochtitlan (Place of the Mexica-Land of Tenoch), of note the place was found by Tenoch the previous ruler of the Mexica.

Unfortunately for them, due to their previous... faux pass, most of the trade within the Valley is closed to them, with no access to building materials or trade, you might imagine that building a city was to be challenging... and it was, they enter into some arrangements with Azcapotzalco who use them in a war with the Chalcans (who will hate the Mexicas from that point on), and eventually hundred-year old evil mummy Tezozomoc Yecatetetetl will grant them princess Ayauhcihuatl, one of his daughters in marriage to Acamapichtli's son, Huitzilihuitl, now the princess in question Ayauhcihuatl is kind of a joke gift as she was too old to conceive child, but due to the massive influence an Azcapotzalcan princess must have wielded her precence convinces other polities to open commerce with Tenochtitlan and allows the Mexica to build up what would become their legendary capital, and eventually they would "adopt" a son, Chimalpopoca, who will be recognized as a son of Ayauhcihuatl, giving the Mexicas access to Toltec blood.

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Chronicle of Mexico by Fernando Alvarado Tezozomoc.