I'm not sure that I would agree a single-ended push-pull output is
significantly easier to bias; linear biasing of "floating" transistors is
done all the time in audio power amplifers, such as are frequently used by
hams at LF; but within the stated parameters of a typical Class D design,
it's not a problem anyway.
As for Peter's question about the bridge configuration, its main advantage is
the same one exploited in bridged audio amplifiers: four times the power
output for a given supply voltage and load impedance. If the power is taken
out via an RF transformer, EACH end of the primary winding alternates between
full supply rail and ground. This is the same as applying twice the voltage
to a winding with one end grounded, without actually having to stress the
amplifying devices with twice the voltage. To achieve the same power in a
non-bridged arrangement, one must go to a lower load impedance and deal with
higher currents; or, change the turns ratio and operate the switching devices
at higher voltage; or some other compromise.
The output of any dual-ended or bridged switching amplifier does not require
the flywheel effect of a traditional tank circuit. The output of the
amplifier is simply a square wave, from which everything but the fundamental
can and should be stripped (with impedance transformation, where necessary).
Unlike single-ended switches, which require resonant circuits with a certain
minimum loaded Q to opreate at all, dual-ended switching amplifiers can be
built to work over roughly an octave without retuning.
The harmonic filtering requirements for a Class D amplifier are not
necessarily greater than for a Class C amplifier. In fact, for single-ended
C, you have to pay a lot more attention to the second harmonic. The third,
fifth, seventh, and ninth harmonics are easier to attenuate than the second.
That's not to say it's trivial, of course! Fast switches produce significant
spurious components up to the edge of UHF, so excellent shielding and
attention to layout and lead length are important. The design isn't that
difficult, but implementation requires attention to detail.
Side note: If a "linear" amplifier is desired with extremely high overall
efficiency, one solution at medium power levels is to use
envelope-elimination-and-recovery. (That was the late Helge Granville's name
for it at Motorola, though I suspect there are other terms in use as well.)
The signal to be amplified is passed to both an envelope detector and a hard
limiter. The hard limiter output becomes the RF drive for the switching-mode
final amplifier, be it Cass D or E or something else. The baseband/envelope
voltage is amplified linearly, although this can be done at high efficiency
too, in an amplifier switched with pulse duration modulation or other
techniques. The amplified envelope becomes the source voltage for the final
RF amplifier. Assuming there are no significant time errors between the RF
and envelope paths, the output can be a highly accurate representation of the
input, as the RF path preserves the phase information impressed on the
carrier and the envelope contains the amplitude information. All modulation
schemes involve varying amplitude and/or phase, so the technique works for
CW, SSB, PSK, AM, QAM, etc. There are some practical complexities, but I
know amateurs who have used it successfully at levels of several hundred