[SteveC]

The main issue for BMW is what is type approved i.e what tyres have been tested and are part of the car's registered safety approval.

In Germany, the 'type approved' tyres are listed in the car's documentation and only those tyres can be used (from a legal and insurance standpoint, anything else is considered not 'roadworthy i.e you wouldn't get an MOT certificate)

Again in Germany, almost all BMWs that specify asymmetric tyres sizes for summer (M- and M-sport cars) specify narrower, symmetric winter tyres on different rims

Economically, buying a 2nd set of wheels has always worked OK for me, ultimately costing me less than a single set of tyres when you consider buying price less selling price after 2 seasons

Add to the fact that the winter tyres in symmetric sizes are way cheaper (due to the production volume and smaller size) and more freely available and the fact I don't have to drive the more expensive rims on salty, slippery roads and for me a 2nd set of wheels makes sense