I understand what common mode transients are. What I don't understand is why they are important at a deeper level.

This Ti app note says that:

Some fault scenarios may include missing pulse, excessive propagation delay, high or low error or output latch, shown in Figure 3

What I don't get is why any of that would happen. Also are there more other/further consequences of insufficient CMTI

Here is what I understand about CMT (particularly for transformer-based isolations):

There exists a capacitance across the isolation (interwinding capacitance in the case of transformers). When large dV/dt events (like switching a high-voltage MOSFET) happen on one side, a current is generated across the capacitor and that gets coupled to the other side through this capacitance.

 

Common mode noise from a switching power supply runs out on the power line, which acts like an antenna and radiates all over the place, blocking radios.
I have helped design several signal generators. If the power supply is pushing 10mV of noise down the shield of the coax cable it effects the output. Maybe you are making 1mV 100khz signal, but it is hidden in 10mV of switcher noise.
Data (TTL) can usually handle 300mV of noise. Data on a DVI cable is 0.34V to 1.38V p-p. A long cable and small data levels causes data errors when noise is added in.

 

So CMTs generate power supply noise? How can that be calculated or estimated?

From a Wurth reference design:

The WE-AGDT Transformer series from Würth Elektronik feature a very low interwinding capacitance down to 6.8 pF, helping the gate driver system to achieve CMTI ratings above 100 kV/µs.

I = C * dV/dt. 6.8pF * 100 kV/us = 680 mA. 680 mA extra current flowing into/out of other side. How does this translate into power supply noise?