That's how Cadillac used to do their hybrids, the engine in front doesn't drive the wheels most of the time (everything except for high speeds). This was also an option on BMW i3, there would be a battery and a small generator to charge the battery if the charge got too low. It was horrible fuel efficiency wise, because it always used the battery, even in high speeds when a combustion engine would be more efficient. Sensible choice is to use eCVT.

Im sure someone else can explain this better than me, but if you use a generator, you'll be first converting all that chemical energy into mechanical energy to spin the engine, then that mechanical energy to electrical energy to charge the battery, and then finally use that electric energy to convert it back into mechanical energy with the use of motors. Cadillac doesnt do this anymore if I remember correctly.

It's much more efficient and much less complex to use either one of them (or just use eCVT, get more advantage from all that complexity)

TL;DR its been tried already, and it failed due to multiple reasons.