The inherit keys are instant transitions, like attachment or draw order keys. When you mix from one animation to another, you can only have one inherit mode. This means the inherit mode is "wrong" for one of the two animations during the mix. After the mix the inherit mode is correct for the current animation.
Inherit keys only affect the animation containing the key, they don't work differently from other keys. By setting a key in the other animation, now both animations have the same inherit mode, so mixing between them won't have this inherit mode problem. If you mix to or from the setup pose, which has a different inherit mode, then you'll see the weirdness again.
You can see this happen in Preview. Turn off repeat, then click one animation, then the other.
Transform constraint has the benefit of being able to mix to/from it, but as you mentioned it has more setup and adds some clutter to the project.
You're right that inherit keys should not display interpolation lines between them in the dopesheet, as they are always an instant change. We'll fix that! They display correctly in the graph.
For other instant changes (attachment, draw order, event keys) we provide "threshold" properties like mixAttachmentThreshold. This allows you to control where in the mix to change from the mixing out animation's attachment keys to the mixing in animation's attachment keys. We will likely add a similar property for inherit mode. It will still be instant, but you can control at runtime where in the mix it changes.
