I think that is massively underselling the disruption to traffic. Depending on the city and the traffic patterns, hundreds of thousands or even millions of people could be commuting into a city on a given day. Reducing the car throughput on a significant portion of roads will cause backups to spread across the road network, affecting thousands.
Maybe switching to bike lanes can be a net positive, but it all depends on the commuting patterns of people living and working the city. Then again, maybe if car commuting is made painful enough, it will accelerate shifts in commuting patterns.
With careful planning the interests of vehicle commuters and cyclists can be balanced for maximum benefit, but I think in the long term changing zoning and development strategies will be what's needed to really make the shift.