One possible path - Look for a common root cause of the firefighting. Make that the next piece of the puzzle to move to your new system. Also, maybe don't delegate strategizing that roadmap to this manager quite yet. Being a good delegator to your reports means knowing when not to do so. Step in, help out to make a plan, and then back off once they are executing the plan.

Another possibility is that they do know how to fix the problem but don't have the resources. This is where jumping in as an IC would help, but that is a band-aid, and a dubious one at that. If they are short on resources, fixing that falls directly into your job. I've seen new directors jump in too much instead of going to the leadership to argue for more resources. It doesn't often go well. Go fight for what your teams need. And if you cannot get the resources for your teams to get the job done, then figure out how to reduce scope. But do not demote someone for problems that are a result of you not getting them enough resources (if that turns out to be the case).