I suspect they suffer from that big government department issue of just very inconsistently interpreted and hence applied rules.
In the past, just getting your friendly local garage to look under the bonnet and say yes, car registration number xxxxxx has engine type xxxxx, number xxxxxxxx fitted, on their own headed paper has been enough. And is sometimes easier and quicker than trying to do it the (possibly correct) way.
As ever, it probably stems from badly thought through rules/regulation, hurriedly applied by those without enough technical knowledge of the department they're in control of. It probably barely occurred to themselves responsible that people actually bought and sold engines legally and legitimately, privately, and then installed them themselves. And even then the thought did occur, they just gave a shudder and added it to the "to do list" under items to be provented for "public safety/greater good/crime prevention et al".