True. Tsukumogami, for instance, acquire conscious life from generations of use and care by humans.
I'm not sure where the concept originally comes from, but I agree that it's common in contemporary Japanese supernatural and fantasy fiction. In many manga and anime, even the power of Shinto deities (kami) is shown to wax and wane with the number and faith of their worshippers. Tsukumogami aside, though, the idea doesn't seem to have roots in either modern/organized Shinto or the older folk traditions from which it grew.
Tbh, I suspect that it's a 20th century, literary attempt to "explain" the fading of monsters, magic, miracles and gods from the visible world. I say this because it's not strictly Japanese. The idea has also long been present in Western supernatural and fantasy fiction in the Weird Tales tradition. It's even there in Tolkien.