Your summary is incorrect. From link from link:

  while the majority of [the savings] consists of traditional transport decongestion benefits, around a fifth are arising from e.g. health, journey quality and safety.

Cycling doesn't replace cars, it just reduces the cost of cars!

Once you're too old, the health benefits are less clear e.g. my mother dangerously broke bones after falling off her bike (I think cause was overloading herself with a grubber in a backpack).