Karatsuba in my understanding only becomes advantageous for very large numbers relative to human scale. Mathematically it is interesting but in engineering terms the overhead usually is not worth it for practical applications. There is a fundamental trade off between factor size and product precision. If you can accept lower precision then floating point works well for large in human scale numbers.
The article discusses how Python uses it for numbers above ~2100 bits for that reason. That’s way beyond your regular floating-point type in terms of precision.