Sounds good to me. I just wonder how the UI would work for this so that it's most convenient. We could have a link to a page that gives a diff of the parent's tags and each of the children's tags in comparison. But that could be inconvenient for actually adding the missing tags, since the user would need to copy the tags they want, open each post, paste them, and remove the +/- signs. This doesn't sound much more convenient than just doing it manually currently.
It might be better if this was worked into the related tags UI somehow. So the user could click a button on the child, and then a new column with a list of tags that the parent has would appear, so the user could click each tag to add/remove it easily. Not sure though, we don't want to clutter up the related tags too much.