size_t vs. uintptr_t

size_t is a type that can hold any array index. This means that, logically, size_t should be able to hold any pointer type

Not necessarily! Hark back to the days of segmented 16-bit architectures for example: an array might be limited to a single segment (so a 16-bit size_t would do) BUT you could have multiple segments (so a 32-bit intptr_t type would be needed to pick the segment as well as the offset within it). I know these things sound weird in these days of uniformly addressable unsegmented architectures, but the standard MUST cater for a wider variety than "what's normal in 2009", you know!-)

Regarding your statement:

"The C standard guarantees that size_t is a type that can hold any array index. This means that, logically, size_t should be able to hold any pointer type."

This is actually a fallacy (a misconception resulting from incorrect reasoning)^(a). You may think the latter follows from the former but that's not actually the case.

Pointers and array indexes are not the same thing. It's quite plausible to envisage a conforming implementation that limits arrays to 65536 elements but allows pointers to address any value into a massive 128-bit address space.

C99 states that the upper limit of a size_t variable is defined by SIZE_MAX and this can be as low as 65535 (see C99 TR3, 7.18.3, unchanged in C11). Pointers would be fairly limited if they were restricted to this range in modern systems.

In practice, you'll probably find that your assumption holds, but that's not because the standard guarantees it. Because it actually doesn't guarantee it.

^(a) This is not some form of personal attack by the way, just stating why your statements are erroneous in the context of critical thinking. For example, the following reasoning is also invalid:

All puppies are cute. This thing is cute. Therefore this thing must be a puppy.

The cuteness or otherwise of puppiess has no bearing here, all I'm stating is that the two facts do not lead to the conclusion, because the first two sentences allow for the existance of cute things that are not puppies.

This is similar to your first statement not necessarily mandating the second.

I'll let all the other answers stand for themselves regarding the reasoning with segment limitations, exotic architectures, and so on.

Isn't the simple difference in names reason enough to use the proper type for the proper thing?

If you're storing a size, use size_t. If you're storing a pointer, use intptr_t. A person reading your code will instantly know that "aha, this is a size of something, probably in bytes", and "oh, here's a pointer value being stored as an integer, for some reason".

Otherwise, you could just use unsigned long (or, in these here modern times, unsigned long long) for everything. Size is not everything, type names carry meaning which is useful since it helps describe the program.