Most architectures do not provide an interrupt that is generated by an integer overflow. Since this would be a significant architectural change in the hardware, it can't be simply added in.
Additionally, if you are running inside an operating system, handling an interrupt usually incurs a trip through the kernel, which would add extra overhead every time an overflow did happen. Since there's a lot of software which depends on integers overflowing, this overhead on each overflow could significantly impact legacy software.
Using a new instruction none of that would be an issue. And as someone pointed out, on x86 it wouldn't even be a new instruction, INTO already exists. But apparently it didn't make it in x64 because nobody used it :/
x86 at one time had a single-byte instruction that would trap if the overflow bit was set, INTO. It doesn't exist in 64-bit mode, I believe, and it was never widely used as far as I know. The performance implications of adding even a single additional instruction to every integer operation were probably still prohibitive? (And there's a history in x86 of specialized clever instructions and mechanisms going unused, due to being slower than doing the same thing some other way.)
Additionally, if you are running inside an operating system, handling an interrupt usually incurs a trip through the kernel, which would add extra overhead every time an overflow did happen. Since there's a lot of software which depends on integers overflowing, this overhead on each overflow could significantly impact legacy software.