Honestly, in well-written C++ you should very rarely see a T** outside of library code. In fact, the more stars you have, the closer you are to winning an award of a certain nature.
That's not to say that a pointer-to-pointer is never called for; you may need to construct a pointer to a pointer for the same reason that you ever need to construct a pointer to any other type of object.
In particular, I might expect to see such a thing inside a data structure or algorithm implementation, when you're shuffling around dynamically allocated nodes, perhaps?
Generally, though, outside of this context, if you need to pass around a reference to a pointer, you'd do just that (i.e. T*&) rather than doubling up on pointers, and even that ought to be fairly rare.
On Stack Overflow you're going to see people doing ghastly things with pointers to arrays of dynamically allocated pointers to data, trying to implement the least efficient "2D vector" they can think of. Please don't be inspired by them.
In summary, your intuition is not without merit.
