This is something I don't get about the code-based CAD tools. They don't let you specify declarative geometric constraints.

Constraints are useful beyond just designing parts. If you have a parallel mechanism there are only two ways to solve the kinematics/dynamics for it: Constraint solving for rigid contacts or iterative solving by approximating the model with non-rigid contacts via internal springs.

Could you mock up some code to describe which you feel would be suitable to describing such a thing?