That's interesting. Personally, I hate the fact that people often use all caps for constants (whether it be #define, const, or enum values). I can accept all-caps for "dangerous" macros, but using them for simple constants is just ugly and unnecessary IMHO.
Of course, if you /want/ to use all-caps for your constants, there is nothing to stop you writing "static const int COUNT = 100;".
That doesn't sound particularly helpful! Even "it's tradition" or "someone else said it was a good idea" would have been better.
And again, personally I /like/ that constants look like normal variables. I don't see a reason to distinguish them.
That is not the point of stronger typing. It has nothing to do with preventing type mismatch - indeed, stronger typing is about using type mismatch compile-time errors in order to spot logical errors in the code.
One day, perhaps, compilers will be omniscient and omnipotent, and such things will no longer be a problem. But then we will be out of a job as programmers (and will be free to join the resistance to fight against Skynet...).
That's fine - it's your choice. You could also consider using enum's for your constants.