I think the main reason for cats in the headers is to get them up to working temperature quicker.
IIRC the Construction & Use regs make it an offence to remove or tamper with any emission control equipment. C & U regs cover a lot of stuff that isn't checked on the MoT test.
Interesting about the Led headlamp change. While looking for further info about other lights around the bike, I came across an assertion that pre-86 vehicles are not affected by the requirement to use E marked replacement lamps, so that maybe makes it "not illegal" (if not actually "legal" to use Led replacements for indicators, stop/tail lights etc. Obviously an advantage on a a 6V dynamo equipped MZ and equally obviously any replacements must be fit for purpose & not dazzle others.