> I assume this implies that common processor architectures (x86_64, aarch64) lack trap-on-overflow variants of their integer arithmetic instructions?

Yes*. But all modern instruction sets have condition flags and conditional instructions, so it's still very much possible to implement the checks robustly in machine code. However, doing so would generally require injecting at least one additional conditional-branch instruction, and in some cases, switching from non-flag-setting instructions to flag-setting instructions (which can be slower).

* = true "trap on overflow" existed in 32-bit x86 but was tricky to use and got removed when going to 64-bit