Until recently, I'd considered the decision by most systems implementors/vendors to keep plain int 32-bit even on 64-bit machines a sort of expedient wart. With modern C99 fixed-size types (int32_t and uint32_t, etc.) the need for there to be a standard integer type of each size 8, 16, 32, and 64 mostly disappears, and it seems like int could just as well be made 64-bit.
However, the biggest real consequence of the size of plain int in C comes from the fact that C essentially does not have arithmetic on smaller-than-int types. In particular, if int is larger than 32-bit, the result of any arithmetic on uint32_t values has type signed int, which is rather unsettling.
Is this a good reason to keep int permanently fixed at 32-bit on real-world implementations? I'm leaning towards saying yes. It seems to me like there could be a huge class of uses of uint32_t which break when int is larger than 32 bits. Even applying the unary minus or bitwise complement operator becomes dangerous unless you cast back to uint32_t.
Of course the same issues apply to uint16_t and uint8_t on current implementations, but everyone seems to be aware of and used to treating them as "smaller-than-int" types.
As you say, I think that the promotion rules really are the killer. uint32_t would then promote to int and all of a sudden you'd have signed arithmetic where almost everybody expects unsigned.
This would be mostly hidden in places where you do just arithmetic and assign back to an uint32_t. But it could be deadly in places where you do comparison to constants. Whether code that relies on such comparisons without doing an explicit cast is reasonable, I don't know. Casting constants like (uint32_t)1 can become quite tedious. I personally at least always use the suffix U for constants that I want to be unsigned, but this already is not as readable as I would like.
Also have in mind that uint32_t etc are not guaranteed to exist. Not even uint8_t. The enforcement of that is an extension from POSIX. So in that sense C as a language is far from being able to make that move.