I was just organizing my stash of vintage stuff I’ve accumulated over the years and realized I have a lot of Biopace chainrings. What I recall is that over time Shimano modified them to be less oval (like Biopace II and Biopace HP) until they gave up and went back to round again. Like others have said racers bad reviews doomed them. My impression was that the concept and engineering worked for recreational riders but sagging sales caused by the reputation they had with fast guys did them in. Unfortunately they weren’t sold as a possible alternative instead of having them across the entire lineup. Shimano was ruthless about getting rid of stuff that didn’t sell no matter if it was better or not (like DD pedals and cranks).
I understand why Biopace was not popular with the fast crowd and why fit recreational riders could benefit from them. Years ago when I rode with the big boys on training rides, I had to have everything perfect (gearing, position, etc.) in order not to get dropped. I didn’t have enough strength to overcome any deficiencies. My cadence had to be higher than when I rode by myself and Biopace rings disturbed my pedaling smoothness. However when I rode with a naturally lower cadence (in the 80’s rpm) by myself I felt like they gave me an advantage.
One of my fellow framebuilders speculated that non-round chainrings might have an advantage because the lower gearing part of the rotation gave the muscles a very slight rest that might have an accumulative effect.