Sorry, I fail to see the point in your second paragraph. Of course in the business logic level you need to allocate variables that can hold every possible value in the valid range, but as long as this is the case, why does it matter that you use types that have the same byte size in every possible platform?
In your third paragraph, i agree on the debuggability front (if you are actually reading memory dumps, otherwise, why should it matter). About the code reading clearer, I guess this is more a matter of taste.
It matters because of code readability, debuggability and all sorts of code hygiene reasons. If I'm using size_t for a field in my protocol on a 32 bit platform on one end and 64 bit platform on the other, which size wins over the wire? Can that question be answered while in debugging flow trying to track down a memory stomping error?
In your third paragraph, i agree on the debuggability front (if you are actually reading memory dumps, otherwise, why should it matter). About the code reading clearer, I guess this is more a matter of taste.