That's already happening.
Finnair ("business light") , Qatar ("P" or 'business lite' fares) and Emirates ('business Special') already introduced unbundled fares in business class that include nothing but the fancy seat and make passengers pay extra for everything from baggage to advance seat selection.
The reason is mainly that business class is increasingly marketed to leisure travellers these days. So,yes, if this catches on BA surely might go down this path as well at some point..