The primary reason, you cannot do bitwise operation on a void *, but you can do the same on a intptr_t.
On many occassion, where you need to perform bitwise operation on an address, you can use intptr_t.
However, for bitwise operations, best approach is to use the unsigned counterpart, uintptr_t.
As mentioned in the other answer by @chux, pointer comparison is another important aspect.
Also, FWIW, as per C11 standard, §7.20.1.4,
These types are optional.
There’s also a semantic consideration.
A void* is supposed to point to something. Despite modern practicality, a pointer is not a memory address. Okay, it usually/probably/always(!) holds one, but it’s not a number. It’s a pointer. It refers to a thing.
A intptr_t does not. It’s an integer value, that is safe to convert to/from a pointer so you can use it for antique APIs, packing it into a pthread function argument, things like that.
That’s why you can do more numbery and bitty things on an intptr_t than you can on a void*, and why you should be self-documenting by using the proper type for the job.
Ultimately, almost everything could be an integer (remember, your computer works on numbers!). Pointers could have been integers. But they’re not. They’re pointers, because they are meant for different use. And, theoretically, they could be something other than numbers.