Bikes just don't take up nearly as much space as cars and don't really block each other as much: gridlock is a problem for cars but not really for bikes. In the Netherlands there are a number of famous intersections where there are no signs nor right of way rules and people on bikes and pedestrians just pass through each other by slowing down and taking turns. These intersection rules were chosen because of the high density: individuals in them can simply deal with the conditions better than formulated timeslots for right of way that waste time while changing priority. Some of these intersections also permit cars but the number of cars in such areas is generally small or limited to buses.
There is a natural limit to how far people want to bike (in a statistical sense, as the distance increases the number of people willing to bike that far drops). The highest density ends up occurring around train stations which is a focal point for foot and bicycle traffic and necessitates large bike parking lots. Those people then switch to trains although they might pick up a bike on the other side. Some people prefer bike rental for these reasons, since when you drop off your bike someone coming the other direction can take it and you can pick up another one at the end of the train ride.
How are e-bikes doing in NL?