Iran gives a case study in why you would want to do so covertly. First, despite having a few allies, Iran is mostly a pariah in the international community. Most major UN states have complied with various sanctions levied against it. Antagonizing said states by openly engaging in acts of aggression simply provides fodder for further punishments.
America is a superpower, and reacting covertly to what are obviously challenges to its power in Iraq is actually more dangerous than responding decisively. As long as the administration feels that it can justify such attacks to the international community, the benefits outweigh the costs. When America was locked in struggle with the USSR during the Cold War, overt aggression was more costly, so conflict usually occurred via proxy actors (Cuba, Afghanistan, etc.).
To put it more bluntly, high-status gorillas use force and threats of force to maintain a harem of females, while low-status gorillas must use cunning and guile to mate opportunistically.
For some, escalating conflict with Iran is the point.