I don't understand why the EASA listed 32/33 applicants are rushing to have their UK ATOs approved by EASA after the 31st December, whilst remaining within the UK. At the moment all UK ATOs are aligned with EASA requirements and this is not going to change immediately. We are yet to know what if any agreements will be made between the UK and the EU. Should there be no agreement then over time there is the possibility of divergence. Once the UK is a 'third country' without agreement then the EASA approval process needs to be assessed as such and at a great expense. If divergence takes place in the future these ATOs will be faced with being one or the other or being a complicated and possibly an impossible mix.
Some years ago during the early days of EASA an attempt was proposed to demand that all EU based pilots and workshops etc, needed to have a EASA approval. This was clearly an anti-american move. It was pointed out by the US that the EASA standards were very different from those of the FAA and it was impossible to simultaneously satisfy both standards. It was also pointed out that the value to the EU from the FAA establishments and personnelle ran into billions of dollars each year. Subsequently the proposals were dropped by EASA.