Indeed. I saw posts of failing MOT in UK in twins related forums too, or repeated tests to finally pass by straw.
And heating up increases those chances. Stock cat on frontpipe should be more efficient, as high-flow are not magically better, just marketed with better sounding name, but in reality are simply of less cell count, less expensive catalizator materials used, thus while less resistive to flow, they also obviously do less for emissions.
As for which cat .. removing primary in header nets most performance gains (but needs ecu tune to disable cat tests to not get CEL), also worsens emissions at cold-start. Decat of secondary is simpler, needs no tune (O2 sensors by which Ecu "tests" cat efficiency are before and after primary cat in header), do better with cold-starts emission tests, but less performance gains, no torque dip elimination as with some aftermarket headers.
But if one were to live in eg. California in US, no aftermarket emission modified bits would go through, failing already at visual checks stage and intake/exhaust bits that would be street legal need separate CARB certification most aftermarket vendors not bother with. Here in LV, with also mandatory OBD2 checks catless header may fail at noticed disabled cat readiness checks in tune.