Why don't languages raise errors on integer overflow by default?

In C#, it was a question of performance. Specifically, out-of-box benchmarking.

When C# was new, Microsoft was hoping a lot of C++ developers would switch to it. They knew that many C++ folks thought of C++ as being fast, especially faster than languages that "wasted" time on automatic memory management and the like.

Both potential adopters and magazine reviewers are likely to get a copy of the new C#, install it, build a trivial app that no one would ever write in the real world, run it in a tight loop, and measure how long it took. Then they'd make a decision for their company or publish an article based on that result.

The fact that their test showed C# to be slower than natively compiled C++ is the kind of thing that would turn people off C# quickly. The fact that your C# app is going to catch overflow/underflow automatically is the kind of thing that they might miss. So, it's off by default.

I think it's obvious that 99% of the time we want /checked to be on. It's an unfortunate compromise.

I think performance is a pretty good reason. If you consider every instruction in a typical program that increments an integer, and if instead of the simple op to add 1, it had to check every time if adding 1 would overflow the type, then the cost in extra cycles would be pretty severe.

You work under the assumption that integer overflow is always undesired behavior.

Sometimes integer overflow is desired behavior. One example I've seen is representation of an absolute heading value as a fixed point number. Given an unsigned int, 0 is 0 or 360 degrees and the max 32 bit unsigned integer (0xffffffff) is the biggest value just below 360 degrees.

int main()
{
    uint32_t shipsHeadingInDegrees= 0;

    // Rotate by a bunch of degrees
    shipsHeadingInDegrees += 0x80000000; // 180 degrees
    shipsHeadingInDegrees += 0x80000000; // another 180 degrees, overflows 
    shipsHeadingInDegrees += 0x80000000; // another 180 degrees

    // Ships heading now will be 180 degrees
    cout << "Ships Heading Is" << (double(shipsHeadingInDegrees) / double(0xffffffff)) * 360.0 << std::endl;

}

There are probably other situations where overflow is acceptable, similar to this example.