Because the position is the head of the military. Normally, you may not want the president to be directly micromanaging tactical decisions because they often don’t have military experience in the same way the head of the defense department usually does. In this case, the system doesn’t work because we have a yahoo hiring other yahoos to do incredibly important jobs.
The real heart of your question, in my opinion, is “why do we centralize power and create vulnerabilities when bad actors can assume those positions?” The answer, in America, is a fundamental mistake by a the founding fathers in believing that all the branches of government were unlikely to be corrupted at the same time, and that they would hold each other accountable when things started to get bad. If the White House became corrupt, the legaslative branch is supposed to stop it. If the legislative branch is corrupt, the court is supposed to stop it. They didn’t concieve of the situation we’ve been in: where all of those branches have abandoned their duties to hold each other accountable. On second thought, I guess you could argue that Thomas Jefferson saw that as a possibility, but his solution was a population that was ready for violent revolution under those conditions. He did not account for the current surveillance/drone/bomb inequality that exists between the people and their government, so his idea was more reasonable for a time where the people and the establishment were able to have equal levels of firepower.
Furthermore, the early constitution placed too much emphasis on the idea that people who are wealthy have a greater stake in the success of the country, and therefore are properly motivated to preserve it (i.e. voting being restricted to land owners). They designed the rules in a pre-global society under the assumption that capital investment in the country equated to the self preservation instinct extending to the nation. Whether or not that was ever true, it certainly is false in the modern world where a rich person can simply move anywhere on the globe that is most beneficial to them in the event of a national collapse.
I have been involved in several cooperative organizations that have no direct leader, and I can anecdotally say that there are pros and cons to both approaches. On the one hand, decentralized and fully democratic power structures definitely keep one bad leader from abusing their power and hurting the community in the process. On the other hand, there is a massive reduction in executive efficiency, and seemingly simple decisions can suddenly take months to finalize while everybody gets their two cents in. That is why most cooperative organizations utilize meeting rules to limit the amount of time a single issue can be debated.
In the case of war, taking a month to finalize a decision can have catastrophic effects, which is why there are single figureheads who have the ability to call the shots quickly. However, as we see now, there is also a massive liability that is created when corruption has been allowed to run rampant and you get a fascist in that seat.