Check your state laws. In OR, a cyclist in a crosswalk is considered a pedestrian. We used to have to maintain a walking speed, but the legislature got rid of that requirement and just restricted us to reasonable speed, which seems reasonable.

If you are not allowed to use the crosswalk, or if you lose your right-of-way by doing so, then that path set-up is a major fail. They would never build an intersection in such a way that motorists can't get through, so they shouldn't be doing it to cyclists.