Both sets of roads are "considered to be safer", because these roads were all selected by cyclists for their regular travel. Were those selected for bike lanes already safer than the others which were not? It is not reasonable to accept prima facie that they were, especially if that's based on nothing more than their selection for bike lanes. You need some study or other evidence demonstrating this.

Secondly, since the physical space is required for a bike lane, it's not reasonable to propose that the bike lane is useless except for the space. It's part of the lane. Adding a bike lane ideally entails adding space for one, if such space doesn't already exist.