Self driving cars won’t fix the real problem - cars take up too much space for the number of people they carry in any reasonably dense city. I’d be quite confident bike lanes should be improving traffic by taking cars off the road more than they are causing “headaches” for traffic.
There are well studied effects that show good bike infrastructure gets more people (especially the young, old, women etc.) cycling who would be too fearful to cycle in traffic, because separate cycle lanes are both in reality far safer but also feel far more safe.
And bike lanes are actually really good for mobility scooters and other kinds of ways for elderly and disabled to get around!