It is entirely possible that the Rito had someone important named something similar to Medoh in this timeline. The reason why the Ruto stuff is important is because it gives us a lot more than just a name. It confirms that the events of OoT occured in this timeline, which did not occur in Child Timeline.
... But all those divine beasts are named after the sages right ?
They even told you in a cinematic i think.
And since one of those beast are named after Medli, it can only takes place after Wind Waker.... That's what i thought at least...
Well, another one of the monuments mentions that Zora's Domain was established 10,000 years ago. We know that Ganon was dormant that entire 10,000 years and Ruto's Zora's Domain had to have been a different place because her story took place long before the 10,000 years ago. Wind Waker never touched upon the aftermath of what happened to the Zoras after Ganondorf froze Zora's Domain since the whole of Hyrule was wiped out, but Downfall makes it pretty clear that Zora's Domain never recovered. So that leaves room for a the new Zora's Domain to be established 10,000 years ago in BotW. In Child Timeline, Zora's Domain never gets attacked and is perfectly fine in Twilight Princess.
I don't know, the only thing that make sense in those game chronologically are the Sages. Since Ocarina of Time the whole concept of "sage" is what put the chronology in the first place... The three others sages makes sense as you pointed yourself, so the fourth one (Medli) should too, there is no reason for this to be "out of the universe" suddenly.... And even less reason to not take that seriously, it's not like map's name which are from the whole franchise and is obviously not relevant. Here, we know from a fact several divine beast name come from the sage and there is no reason to think it's not the case for the others ones, especially as Darunia is so easy to guess.
Also in the book, there is a whole page about Zora and the fact they become uncivilized civilization in the downfall chronology and only there, it makes no sense for them to still have an history in Breath of the Wild.
Even the whole idea of having an advanced technologically Zelda can be a better follow up to Spirit Track than... Any other episode really. The only argument against BOTW not being in the Adult era that i see is that Ganondorf only appeared "once" at the end of Wind Waker and then other villain took the crown... But i don't see that as convincing, maybe Link really killed Ganondorf at the end of Wind Waker and his ressurection totally wiped out his human consciousness at this point since it's been so long... It works for me at least, there is far stranger stretch in the chronology...
I think people want to put it in the Downfall chronology because it's somewhat "elegent" since BOTW is kind of a follow up of Zelda 1... But there is really no reason for this to be the case, every serious lead point to be the follow up to Wind Waker the more i think about it. (Oh, and of course that "Hyrule" isn't flooded since we are on a new continent)
Edit : And even in the Sacred Realm, the power of the Goddess can still be used, i think that's what the triforce stuff at the end mean. It's not as if we have access to the triforce in order to make a wish... Or anyone trying to get it for that reason, the Triforce is really a power "out of this world".... Defenitly my most stretchy argument, but i still think it makes more sense than the Downfall one.
I maintain that the actual Triforce never actually appears in BotW. Zelda's power is the goddess power of Hylia, which every Zelda has had and never involved having the Triforce. A Triforce mark does appear when she uses this power, but glowing Triforce marks have been fairly abundant in the series without representing the actual Triforce. In all past games involving the actual triforce, once the whole Triforce is completed it exists out in the world as a solid 3D object that one must touch in order to wish upon. But the power Zelda uses is just an energy blast with a flat Triforce mark.
Zelda mentions she has a power passed down in her bloodline that can defeat Ganondorf, and the Triforce features in the closing cutscene accordingly. It's one of the reasons that this game is probably not in the Adult Timeline, since the Triforce is in the Sacred Realm by the end of tWW and can't be accessed without major hand-waving.