The arguments against zero crossing switching transformers applies to primary of secondary. The claim (largely borne out in practice) is that the core saturates when subject to the rising voltage while unmagnetised. This is generally not an intuitive outcome. It makes sense when you consider that in an inductor under steady state conditions voltage and current are 90 degrees out of phase. By switching the voltage on at the peak of the voltage waveform you have maximum voltage and zero current so the 90 degree relationship is automatically established as the initial condition. You still need to build the "magnetising current field" but you are at the best starting point.
Nicely summed up in the final reference below:
Instead, it would be better to close the switch at the peak of the
input AC line voltage. Since the inductor's current is initially zero
as before, switching this way puts the applied voltage and the
inductor's current immediately in quadrature with each other (or
really close to it) and there is no transient event or current
The current starts out already settled.
At a minimum what happens is that the current waveform is offset relative to zero so that a current sinusoid DC offset by Ipeak/2 initially occurs. This leads to about double expected peak currents if the core does not saturate - and some sources suggest even higher initial surges, due to saturation effects.
The subject is covered reasonably well in Rod Elliots inrush current -
and especially section 4. "Inductive & Transformer Inrush".
Useful paper here - less severe claims
Effect of Switching angle on Magnetizing flux and Inrush current of a Transformer
(ie saturation effects not dealt with)
Open electrical wiki - transformer inrush
Some practical experiences reported here To Zero Cross or Not To Zero Cross.
Some years back, I was the project engineer on a large component
burn-in system. The system was supplied off of a 3-phase power
transformer so that the loads could be as balanced as possible. I had
designed TRIAC controllers to ramp up the line voltage to minimize the
line surge with +90 degree phase shifting. Each power supply was a
very large, 50lb, power transformer with multiple secondaries. To tell
a long story in short, the 'chief' engineer insisted on replacing the
three small power transformers I had specified with the one big
monster and he also insisted on using zero cross over phase control to
minimize the current surges despite my arguing for the other method.
To him, zero voltage across the primary meant zero current....
The PC boards were finished per the Chief's changes and a few power
supplies were built. When they were switched on, there was a snap and
flash of light in each one of them, a PCB trace was vaporized due to
the huge magnetizing current resulting from the zero cross over phase
control. Since the boards had already been built, modifying them was
out of the question, the only thing I could do was to place a large
ballast resistor in the primary to limit the current surge. The Chief
refused to accept the premise that it was his zero cross over and
monster power transformer causing the problem.