My understanding was that Paradoxes and the like were mainly designed for use on cats. However, I had not seen that advertisment for the 10 bore! They were still being used well into the 1960s. John Kingsley-Heath had one made by Purdey.

This is just an educated guess, but part of the reason that they went out of use may be down to British firearms law. Here, there is one licence for a shotgun and another for a 'firearm' (rifles and pistols, until the latter were banned). As a paradox is a bit of both, this may have caused much scratching of official heads when the British laws began to become more restrictive in the 1960s. For the same reason, drillings are uncommon here.

I do have a 12 bore paradox round in my colection and it is huge!