> A check is only useful if you want to actually change the behavior when it happens, otherwise it is useless.

You almost always want to change the behavior to erroring out on overflow. The few cases where overflow really is intended and fine can be handled by explicit opt-out.

And I refuse to buy the argument that "small things add up" in the world where we do string building and parsing every few microseconds. Checked math will have unnoticable impact compared to all the other things we do, in almost every type of program.