It is this latter point that is relevant. What is the MOT failure rate due to failing emissions testing?
Failure rate for old cars in emission tests (just like any other reason) is significant and after simple fixes many still pass.
Like,
* Leaking exhaust, no actual problem with emissions, air that mixes in increases O2 and fails measurement
* O2 sensor failing, new sensor takes a few minutes to swap and costs like $50 or even less for a cheap aftermarket part which lasts for another year or two
* Carburetor mix ratio knob misadjusted, takes a few minutes to correct
No one scraps a car just because it failed, failing is completely normal even for new cars. Of course if the car is really in bad condition and the owner has been thinking about scrapping it anyway then failed inspection can be the final straw. Of course as an exception to this rule, ugly surprises can arise like engine block needing expensive/specialized work (boring, etc.)