BTCC also artificially manufacture closer racing by imposing weight penalties on cars that are faster on the day. That works in BTCC but I don’t see that being transferable to something like F1.
As for same spec cars with identical engines, anyone remember A1 GP? No, thought not.
Forcing F1 down that route of standardising the cars would largely defeat the purpose of F1. Aside from the fact that it’s a team sport, and therefore reducing it so that the only difference is the driver removes the team aspect, it’s also supposed to be the pinnacle of racing. By providing all the chassis and engines for the teams undermines the basic principal of development that is the foundation of F1. I mean, how much tech on your average daily comes from BTCC, after all?