> There aren't a lot of options when you need to have cars turning on roads with bike lanes. At some point the car lane and the bike lane have to cross paths unless you're going to build a fully grade-separated bike lane.

The problem is that the lane markings encourage vehicles to make turns from the non-rightmost or non-leftmost lane. One should not be crossing another lane when making a turn at an intersection. One should merge into the rightmost or left most lane in order to make the corresponding turn.