Rectifying AC doesn't make much sense: the advantage is small while the cost is relatively large (and, not that rectifiers and capacitors are exactly expensive themselves, but like I said, the advantage is just that small).
The advantage is larger for low-level stages, guitar pickup, phono, etc., where the ripple makes a bigger difference. The cost of a simple rectifier-filter is more acceptable, too (i.e., rectifier, cap-input filter, RC filter to heater -- R necessary to adjust voltage down (can get some extra filtering out of it too), wasting some power).
DC bias also helps, to reverse-bias the heater-cathode diode. The heater still has some emission, and this helps reduce current flow in general -- thus reducing ripple input as well.
You could go fancier and use an SMPS, but 6.3VDC is somewhat uncommon, and if you're going to go the trouble, why not make the 300V or whatever with it too? But now you're doing an entire power supply design for very little amplifier, and EMI is a real problem.
Tim