I have checked STR() usage in my application but usage is safe because we are not dealing with more than 12 digit number.
May I suggest that if numeric integrity is truly important to your application, you either:
A) switch over to a deterministic method of converting from the current nondeterministic one
B) Run a comprehensive test (i.e. verify that every single number from 0 to 999999999999 does, indeed, return what you expect when you use the STR() function), probably from the largest and most risky number to the smallest, ensure all STR() use cannot end up in 13 chars or more, and comment all STR() code with this note, a short description of the flaw, and a link to Jeff's article. You don't want some bright-eyed person later on copying this "perfectly fine, working production code" later for something larger, or updating it with future business requirements.
B1) Repeat your tests every upgrade... just in case.
I expect nondeterministic functions to be nondeterministic. If I want reliability, I choose something that's expected/known/documented/empirically shown to be deterministic.