The output amp being class B with noticeable xover dist is really unacceptable in a serious function generator.
Well, blame Texas Instruments or Analog Devices - whoever make them.
And I haven't seen any integrated wideband OpAmp that is not class B in a long time.
If you need an ultra low distortion audio oscillator, there are dedicated devices for that, although with very limited frequency range.
We always had that distinction: Audio Oscillator vs. Function Generator.
Analog function generators had distortion figures up to 1% THD at any output level, so crossover distortions certainly have been a minor concern there.
Like any function (or signal) generator, modern digital AWGs operate at high output levels and use attenuators to get the signal down to the desired levels, so once again crossover distortions are a non-issue, even though the THD figures are much lower than on their analog counterparts.
For the setup I've described in my earlier posting, no crossover distortion will be noticable either, since both output amplifiers operate at reasonable levels. The THD for the SDG is specified as <-65dBc up to 1MHz, I've measured some -80dBc at 20kHz, not as good as a 16bit system could ideally be, but still very good for a function generator.
Of course a good soundcard in conjunction with an external step attenuator will be much better for high-end audio.