Not using X2 rated capacitors in AC filter for offlien SMPS?

Thanks, and generally I tend to agree. In other words, generally speaking it is usually better to put the mains filter downstream of the rectifier bridge because then the capacitors can usually be smaller and cheaper....because its DC and not AC.
However, the X1/X2 rating doesn’t come into this discussion..because the X1/X2 rating pertains to its ability to be able to handle mains voltage transients. And a mains voltage transient is going to be just as bad for a capacitor situated upstream or downstream of a rectifier bridge……so why are the capacitors of the document in question (in post #17 above) allowed to be non X1/X2 rated?

These capacitors are not going to be protected from mains voltage transients by being situated downstream of the mains rectifier bridge, so why are they allowed to be non X1/X2 rated?

Transient rating of the DC capacitors is of course a question of interest. Just wanted to emphasize that X2 specification is particularly for AC capacitors. Required specification for the DC filter capacitors is a different question.

I think you need to know what safety standard applies to your design.

I'm guessing non-X1/X2 rated caps are permissible across mains if the available power is low.
First realize a film capacitor failure is not just open/short but can fail into a resistive state, like an old MOV.
Not enough to pop your mains fuse but enough current to burn up and be a fire hazard. I think this how regulatory views it.
Some standards have power levels where you get an exemption. But most are calling for X1/X2 rated caps.

Consider looking at LED lamp teardowns. Many seem to be using using ordinary film caps across the line.