What is the thought process for specifying an EMI bypass cap on line transformer secondary?
You don't want just capacitors, you want to install an RC snubber on the transformer secondaries.  The reason is that when the secondary voltage drops far enough that the diodes stop conducting, you would get significant ringing due to the interaction between the diode's open-circuit capacitance and the transformer's inductance.  Here is an appnote on snubber design but it's fairly technical and assumes you know more about the transformer than you are likely to actually know.

A capacitor alone is likely to make the ringing worse.  A resistor is necessary, as it is the component that dissipates energy and therefore reduces the Q of the LC ringing.

The exact choice of R and C depends on your selection of bridge rectifiers and transformers and the most accurate way of designing the snubber seems to be empirically, because of all the unknowns in buying a random transformer from the shop without a super-detailed datasheet.

Have a look at this diyaudio thread, where they describe a device to drive the transformer with impulses and thereby measure the effect of the snubber.

My vague recollection of when I last designed a transformer snubber was that the choice of R is important in terms of getting Q down to where you want it but you don't need to be super-precise, and the C (in series with the R) exists merely to prevent the R from dissipating loads of power at 50/60Hz.  So you might be looking at a few hundred ohms (totally dependent on the transformer!) and about 100nF of C, but the exact value of C doesn't matter much at all.  C just needs to be big enough so that the RC impedance is very close to R at the ringing frequency, and "high" at 50-60Hz.