You don’t have to be wealthy to pay to use them, you just have to value the time savings more than others. Imagine a “poor” person late for their job where they will get fired, they might value the lane more than a “rich” person just cruising around for fun. Whereas if it weren’t an option at all the poor person in this scenario loses their job and is strictly worse off.
I feel like you dont live in the bay area. In peak traffic time, those lanes cost like $20+ to drive in.
Your assumption that rich people spend less for fun than poor people can afford to spend to survive is not something I think I'm confident enough in to trust it as the basis for policy like this.