Yes, some special forces cover their faces, but, not all special forces around the world are not covering their faces. That especially means military special forces. It’s quite a different situation with the police special forces (SWAT units). It is a difference between military and law enforcement tasks, and there lays the answer to the question. Why don’t the US Special Forces cover their face like other special forces around the world?
In military cases, it’s simple. Why would they cover their faces? Does seeing their face compromise them? Think about it, some random person in a third-world country sees a guy in a uniform. Ok, so what? For example, the US Special Forces are not covering their faces in most cases and it is easy to explain.
Out of all of the US people, what are the chances that you can track down that specific guy based on having seen his face? In fact, if you see the guy in full combat gear, you probably don’t get to see a whole lot of his face anyway. Ok, here’s his picture. Now go back to the US and try to find this guy. BTW he probably won’t have the beard anymore. Good luck with that. And to a foreign national in a non-European country, there’s a good chance that all guys look alike.
More importantly, many SF’s primary missions, such as foreign internal defense (FID), training foreign militias, or providing humanitarian assistance, require them to interact with foreign nationals and build rapport with their partners. How well do you react to some guy walking up to you in a mask and telling you what to do?
Now, if you see them on a combat patrol or in a direct action mission, they may have their faces covered, but it’s probably due to other considerations like the weather or breathing in dust rather than a need to conceal their faces.
It’s different from special police units around the world. Imagine working in a city where everyone knows everyone etc. cities with less than a million inhabitants. And your tasks vary from apprehending high-level criminals, execute high-risk arrest warrants, or so on.
So, you could easily be identified, and sometimes, somewhere, someone could try to get revenge. SWAT tasks differentiate from regular patrol officers. Their modus operandi is harder than regular police, so basically, most of such units must cover their faces and conceal their identity. Most of the European special police units using various types of balaclavas to cover their faces, and those balaclavas could also be seen as part of the protective gear.