I put together a real-life circuit representing your sim: 6.3VAC/6A transformer, 3A/40PIV schottky, 6.8mF filter cap and 100mA avg DC load.
Output: 8.5VDC, 64mV RMS ripple, 250mV PP ripple
Pics of scope:
Ripple waveform with scales adjusted to emphasize apparent nastiness of it similar to what you posted:
Ripple waveform with original 6.3VAC superimposed, both at same scale:
AC output of 6.3VAC transformer with hipass filter and 70mA AC load:
All things considered, I'd take the DC with a little bit of sawtooth ripple over the noisy, 100% ripple power line source for heating an IDH tube hands down. And this is with far less than optimum half wave rectification. Others may choose differently for a variety of technical and aesthetic reasons.
