Maybe the Senju can read it as well in some different way, or they have other ways to follow a certain path.
Maybe the Elder son did something to the tablet to make sure only the Uchiha were benifitting from it.
We dont know. There are to many blanks imo to say that the sage only left it for the Uchiha.
Naruto in a way is following a certain path and he can only do this, because he has not read the tablet I think.
If he had read it, he might have followed a different path, so in a way, it is a good thing that he didnt read it.
So maybe the sage did it on purpose. Maybe he felt it would benifit the younger son more to not have read it.
But again as I say, I feel there are lot of blanks still.