If you want to look at the problem yourself, compare how an IK constraint is applied (the math looks crazy, and it is, but step through and you'll see most of it can be ignored for the common cases) versus a transform (much simpler to look at) or a path constraint. Path and transform constraints work solely on the world values (bone matrix and world position), they don't use the local values. IK constraint uses both the local and world values. Now consider:
1) Apply a transform constraint. The bone matrix and world position is adjusted.
2) Apply an IK constraint. First, it uses local transform values, so won't see changes the transform constraint made. Second, after finding the IK solution, it does updateWorldTransform
to compute a new bone matrix and world position, which will overwrite the transform constraint changes.
Solving this means either:
1) Transform and path constraints need to work by adjusting local values rather than world values. This is difficult because these constraints really do manipulate world values, so their manipulations would have to be mapped to local values, which can be ambiguous. See updateLocalTransform for what that might look like.
OR
2) IK needs to work without using local values. This is difficult because IK needs to translate the child and target bones into local space to do the IK solving, however this is probably the most sane solution.
If the solution involves extra work, possibly we can find a way to avoid that work when it isn't needed.