Why all this happens?
It happens because almost everything has been made lossless and ideal.
Speculation: When the simulator makes a small error in the on-time of the
output diodes, the secondary leakage inductor currents store some energy
that can go nowhere when the output diodes subsequently turn off again.
That is an error (more than) 2 timesteps back, and normal SPICE is only
able to reject the current timestep. The way to get the right results is thus
to make very small timesteps, which is correct but we don’t like the
consequences.
The RC circuit only works for superhigh-frequencies because of the small
value of the series capacitor and dissipates the excess energy in the
leakage without taking significant power from the load.
Trap-ringing is nothing special. Because the trap algorithm has an error
that oscillates between its min. and max. value instead of exponentially
decaying, the human eye “sees” this error. The trick of smoothing the
signal (modified-trap) is nothing but eye-candy (the error is still there).