Tyranitar never felt right for her because it's the gen's pseudolegendary and those are more appropriate for the gen's Champion.
actually let's run the numbers
kanto: lance (4th elite) has dragonite. blue doesn't. 1-0.
johto: neither the elites nor lance have tyranitar... lance does have 3 dragonites, so 1-1
hoenn: the region with two late bloomers and, accordingly, drake (4th elite) has salamence and steven (champion) has metagross. in emerald wallace doesn't have any, though. 2-2
sinnoh: cynthia (champion) has garchomp, the elites have no previous late bloomers. 2-3
unova: in BW, hydreigon is actually ghetsis's, so... nobody. B2W2 has iris (champion) with hydreigon, but also grimsley and caitlin (elites) with tyranitar and metagross, but only on rematches. giving this one to iris because hydreigon is always there (and because volcarona is very late bloomer-coded and is alder's signature pokémon and i love volcarona lol). 2-4
kalos: diantha (champion) has goodra, the elites have no previous late bloomers. 2-5
alola: no elites, prof kukui or hau have ANY late bloomer, which is a disappointment for a region with so many available late bloomers, even if kommo-o was a totem battle. 2-5
galar: leon (champion) has dragapult. but also, raihan (last cup battle before leon) has goodra. 3-6
paldea: hassel (4th elite) has baxcalibur from the main game. geeta only gets a dragapult by indigo disk after many allegations of sucking ass. 4-6
unova-blueberry academy: amarys (elite) has a metagross, drayton (elite and former champion) has a dragonite. the champion has a dragonite, too, which... there Are other late bloomers out there... anyway, 6-7. makes sense for a post-game elite four.
i'd say they are equally likely to be associated with the last elite four member (specially in games in which the elite four battling order is fixed) as they are with the champion.