Well that's only half right in the lore. After the manga and Goku's death in Age 801 (most likely by old age since he and Vegeta left Earth to have one more fight and were never seen again), Gohan released a book called "Groundbreaking Science" that explained the fundamentals of ki to the Earth's population. I believe it wasn't that Humans could control ki to the same level as the other races, but simply because they were ignorant about it (Mr. Satan aka Hercule didn't make things better). Now granted they aren't as "good" with it as Saiyans and Namekians, but that doesn't mean they were weak. Tien is a prime example of this when he was using Shin Kienzon (Neo Tri-Beam) to stall Semi-Perfect Cell. Despite being heavily outclassed in power, Tien was still able to perform a feat on an opponent who was stronger than a normal, untrained Super Saiyan.
Now the issue with Humans in DBO is the fact that our CaCs are descendants of the Son/Brief family. As such, while our CaCs Saiyan blood is pretty much gone, the potential that goes with it remains and simply requires unlocking it. This was something that Dende was actually counting on when he reactivated the DBs and made more of them while placing huge restrictions on what the user can wish for.
That doesn't disprove my point. I never said Humans couldn't learn to use Ki with the same efficiency, I simply stated that, from what we know about the Dragon Ball lore in general, Humans were never gifted in terms of Ki usage to begin with, we would've seen some Humans actually break through their limits if that was true, yet they never reached the level of power of Saiyans,Namekians and other alien races. I accept the point about Tien, but since in the Daizenshuu it is stated that he is a descendant of an ancient alien race himself, I can't fully believe it, as it makes him compared even more with our Humans in DBO; not only that, you always need to keep in mind that Dragon Ball is a work of art, and to me, Tien's Shin Kikohoo on Semi-Perfect Cell, as badass and beautiful as it was, was fanservice, I may be wrong, but that's my opinion(he got one-kicked by Buu without problems, later in the Buu saga). Gohan simply gave the Humans the means to use Ki in the most efficient way possible by introducing them to the "alien level" of Ki knowledge, where as before, Ki on Earth was mostly limited to fighters and monks like Muten and the Orin Temple. That is later supported by Pan's TV show, and Tien's and Krillin's new schools.
Game balancing aside, it would actually make sense for Dende to put limits on the Dragon Balls, it was a security measure, what would happen if the Red Pants of the Time Breakers were to find the Dragon Balls?
We saw Goku/Vegeta Jr. do that in GT. Putting aside personal feelings for that series, DBO is based strictly off the manga. Anything that was anime only is excluded. So you can't use that for lore reference purposes in DBO related content.
So all we have to go on, is Pan at the end of Z, in terms of what happens the more and more diluted the Saiyan blood gets vs potential of lost power. And it's a perfect example of why the training is what matters in the time of DBO, and not the transformation it self.
I still don't see the point. At the end of Z, it is never stated, manga or anime, that Pan diluted Saiyan blood can't make her achieve the transformation, she is simply never shown to use/achieve it yet. Hell, she even punches Goten in the face. And we all loved that.