I'm currently replaying Skyward Sword, where I just ran into the Gossip Stones again, which had me thinking... In the 3D Zelda games that have Gossip Stones they were usually a great way to explore the world even further. Well, in Skyward Sword they are more of an ingame "tips and tricks" section, but at least in the Nintendo 64 Zelda games they delivered information about the world and its people, which you couldn't have gotten otherwise. Interesting details.
And since Breath of the Wild is all about exploring, having hidden Gossip Stones around the world could be part of it. In this case we could get like a modernized Sheikah technology version of them, where they are activated and read by the Sheikah Slate. This makes sense, because the original Gossip Stones were apparently left by the Sheikah, judging from the symbol on them, and could only be read via the Mask of Truth.