I don't think saying China didn't see and learn from the failing aspects of American city planning is fair or useful, especially when it comes to road planning. The Chinese and American culture on road use is completely different: (power/gas) scooters and (regular) bikes are extremely popular in Beijing, and Chinese drivers are generally much more aggressive. Because of this, most road users, including bikers, are capable of driving defensively against other road users. Most bikers/scooter-ers are already comfortable with weaving between cars on their commute. Would a segregated lane make commuting on smaller vehicles safer? Undoubtedly. Would it be necessary to incentivize biking over driving larger vehicles? Probably not.

This, along with other problems, like an exponentially expanding middle class population that can suddenly afford vehicles, is only one of the many different challenges most western governments have not experienced, which China currently faces. It may be unfair to quickly jump to conclusions and simply say the Chinese have not learned from the history of urban planning by western countries, when there are very few references from which the Chinese government can draw on, for the unique problems that they are facing.

TL;DR: Chinese urban centers have problems that cities in Western countries have not faced.