Sometimes in colonial America, people named things in honor a Duke who funded/controlled the place.
For example, after NY was captured from the Dutch, it was a proprietary colony of the Duke of York.
Better York sounds like it's just antagonistic towards the guy.
I don't think you'll find anyone who suggests that bikes as a single mode of transportation is the solution.
No single mode of transportation is the solution. The solution isn't "subways". The solution isn't "busses". The solution isn't "trams". Or "cars".
Instead, in cities, the solution is a mix of modes. Sometimes that's using one mode locally and a different mode to get across the city. Sometimes that's multimodal trips - taking a bike to the train then biking the rest of the way, for example.
Bikes are particularly good at solving the "last mile problem", which public transit is pretty lousy at solving. That's why, if you go to train stations in the Netherlands they have bike garages. Because trains and bikes are better than trains without bikes and bikes without trains.