First, let me say that I view an organizational structure as a command and control network, which filters information on the way up the structure and expands information on the way down the structure. I like the horizontal organization structure, but realize that there are limits on the number of relationships a person can manage. Effectively, we are pre-wired to manage approximately 150-200 relationships (span of control) (R.I.M Dunbar, "Neocortex size as a constraint on group size in primates," Journal of Human Evolution)(1992), vol. 20, pp. 469-493).
Now for my analysis of your question:
From an organizational viewpoint, I see a minimum of 21 standard direct reports (information streams - the cabinet & cabinet ranking members) to the U.S. president. This does not count the NSA, the leader of the intelligence Org, who does a daily briefing, or other special study groups. Therefore, we can conclude that there are 21+ channels of organizational filtered information flowing to the president (the decision maker). The span of control is higher than a typical business, but should be reasonable given the number of relationships that a human can handle. Therefore, adding another direct report should NOT be an issue.
This organizational structure (chain of command) establishes priorities on the information flowing through each channel. In other words, some of the information, which may be important in understanding the overall picture, is filtered as it moves up through the organization. To resolve the filtering issue, organizations have historically established alternative paths of communication to the key decision makers for highly important areas of concern. This is accomplished by creating task forces, special studies groups, etc. Therefore, I conclude that if you want to limit organizational filtering of information, then an alternative channel of communication must be established, which bypasses the standard organizational structure. Therefore, if the objective is to reduce/limit the filtering of information on the war(s), then an appointment of a War Czar (Most likely a media label) or a Deputy National Security advisor is an appropriate action to take.
Keith Morgan