This apparently starts in May 2018 as a rolling exemption in parallel with road tax, but the caveat is the cars must not be 'substantially changed' which is based on the DVLA's 8-point rule with guidance to follow. MOT exemption was considered for 30 year old cars, but didn't make it for similar reasons to the 30 year road tax exemption. There is a bit of a 30 year anomaly 'We have decided that we will consider only modifications made since 1988 when determining whether a vehicle has been substantially altered and thus not exempt from testing'. So pre 1988 completed GTI Engineering cars are in the pound seats there. There's much more detail in this Government Response to Exempting Vehicles of Historical Interest from Roadworthiness Testing - pdf The 8 point rule is a potential knock to converting an automatic car since you loose 2 points for a transmission change.
Yeah bureaucracy is boring, but I do find the reasoning interesting. It's typically big picture and not without counterpoints. For example cars registered from 61-73 (a large proportion of the 61-77 12of16 years) have enjoyed tax free status since 1997 which is a massive boost to the maintenance budget and the status also helps in itself. What about the accident data from cars either side of the line 72/73. The number of cars 78-87 that would be classed as 'substantially changed' and so irrelevant to MOT exemption. Probably equally boring, but there you go.