Roads may not have originally been designed for cars, but that is what they are for now. You can make a philosophical debate that they shouldn’t be, and I would agree with you, but that is our shared reality.
The issue then is that cyclists are frustrated because they feel they have the same right to the road as cars do and drivers are frustrated because all but the most elite cyclists simply cannot keep up with posted speed limits.
The answer is full separate lanes either elevated or with a curb or barrier. We have them for pedestrians, we have them for cars, why not for cyclists where it makes sense?
It would be expensive, especially initially, but in cities it could help alleviate traffic congestion.