> arbitrary precision is often the completely wrong tool, e.g. it would make certain key algorithms (like Gaussian elimination) exponential.
Sure, but even in science taking a lot of time to deliver a result, or failing to deliver one at all, is much safer than silently delivering the wrong result. There's the concept of fail-stop if you want a rigorous approach to safety. There's no analogous safety model that says silent overflow is the safe option.
Maybe for LOB applications, it would be better if languages defaulted to arbitrary precision arithmetic. But scientific computing is also a huge field that often uses the same languages and there, arbitrary precision is often the completely wrong tool, e.g. it would make certain key algorithms (like Gaussian elimination) exponential.
I feel like this is just one of these things that developers should know about so they can make the correct choice, just like DB indices.