> Exposing exp2 in the math library would be less interesting

I disagree: a libm exp2 is likely to be significantly accurate than pow(2.0, x). The latter is unlikely to be special-cased by the libm pow.

> The latter can call exp2() internally if it provides more accuracy than exp(log(x)*y).

It would be a very poor pow implementation that used exp(log(x)*y).