We kind of already do. For example, there is the INTO (interrupt on overflow) x86 instruction, which calls an interrupt if the overflow flag is set. Nobody ever uses it, though. Probably because it saves you nothing over just using JO (jump on overflow) after every arithmetic instruction, which itself has so little cost (overflow doesn't usually happen, so the branch will almost always be predicted) that many languages have compilers that already do this by default.
But C is a terribly primitive language. If I remember correctly, unsigned integers don't really have overflow; the result of any arithmetic operation is supposed to be modulo whatever the maximum is. UINT_MAX + 1 is required to be 0. Signed overflow is supposed to be undefined, but I suppose C programmers care more about saving one instruction plus a usually-predicted branch than they care about making programs more reliable. Of course, a lot of programs depend on signed integers behaving just like unsigned integers, so fixing this would be painful.
But C is a terribly primitive language. If I remember correctly, unsigned integers don't really have overflow; the result of any arithmetic operation is supposed to be modulo whatever the maximum is. UINT_MAX + 1 is required to be 0. Signed overflow is supposed to be undefined, but I suppose C programmers care more about saving one instruction plus a usually-predicted branch than they care about making programs more reliable. Of course, a lot of programs depend on signed integers behaving just like unsigned integers, so fixing this would be painful.