Whenever I looked at several CWA ballast wiring diagrams, I have noticed that not every CWA ballast has a capacitor wired in series with the lamp as many of us have been told. In the case of most North American high pressure sodium and pulse start metal halide CWA ballasts, the series capacitor is actually wired between the autotransformer coil and the reactor/choke coil. I wonder why the capacitor of such CWA ballasts is wired this way considering that these ballasts all use an impulser ignitor tap on the reactor/choke coil?

The attached photo shows a wiring diagram of such ballasts.

During normal burning, the ignitor is supposed to be completely "inert". If you remove it from the circuit, you will see the capacitor is still in series with the lamp and the transformer secondary, the same as with the ballasts without the ignitor. So there is no topology difference between these two arrangements.
The reason why with probe start ballastsit was in the lead to the socket is to make the transfomer assembly with fewer external leads, simpler to use (the connection to the primary tap thencould be made directly within the transformer primary).
The reasons why the same isn't used with the pulse start ignitor are actually two:
First the lamp output has high voltage pulses on it, so if that were connected to the capacitor, the xapacitor would have to withstand such voltage between its mainfu ctional core and the shell (or its mount). Mainly with metal case capacitors that would be a problem: It would require special capacitor construction, which would be a bit more expensive, but mainly it would "be asking" for an installation error where someone would use standard capacitor not able to handle that voltage there.
Second reason is, it would place an extra component to the primary circuit of the HV pulser (C, sidac, ballast winding section between the tap and the lamp end).
Placing the capacitor iinto the secondary cold lead solves both issues, it just needs two extra wires from the transformer assembly.

I always assumed that the capacitor of pulse-start constant-wattage ballasts was connected before the choke section to place it outside of the ballast section exposed to HV pulses, which are coming from said choke when the ignitor is active.

But Medved's explanation is pretty exhaustive!