You’re right, my mistake. But for example, the BMW 530e G60 does have a button to charge the battery from the engine, and it is a PHEV. So it does exist.

It depends, some use the engine to charge the battery (e.g. the Honda Civic).

I think the point is that PHEVs do not achieve the real world emissions promised by the manufacturers, which would call into doubt reliance on them to save the climate as well as tax reliefs. Particularly, company cars are historically subsidized too much, and they get even more subsidies if they are hybrids, only to then never charge them.