I'm trying to separate out which is "don't do this in C/C++" and which is "don't do this in any language".
To achieve high performance, any language would need to implement integer addition with a single machine instruction like 'ADD'. Languages can achieve more intuitive behavior by adding an operand check before the 'ADD', or by using an 'ADC' instruction and checking the carry bit afterwards. But adding branch statements to every add operation would slow computation significantly. Clever languages/compilers might deduce certain invariants and variable ranges that enable it to remove some of these branches to help in certain special cases.
Evidently Rust has an optional "safe add" that adds the branches to check for overflow. So newer languages offer more explicit options. But the core issue is more fundamental than language-specific.