Sure, but:

1) As soon as you wrap it in a Python class, much of that speed advantage goes away.

2) Double-double doesn't solve the problem with the limited exponent range of doubles.

3) When the goal is to allow setting the precision to any number of bits you like, having a separate implementation for X bits complicates things a lot, especially when the X-bit arithmetic doesn't quite behave like Y-bit arithmetic for X != Y (double-double behaves somewhat differently from 108-bit floating-point).

IMO, double-double would be most interesting as a NumPy extension.