The problem with solutions such as this is that there's no way for the computer to pre-determine what would be a "vantage point" or "cover" (at least not without significantly powerful algorithms). It works in games like FEAR because that kind of thing is tightly controlled and pre-determined by the level designers, and they have highly complex pathing and decision-making structures to support it.
A more feasible solution for Doom would be to have monsters "think" about possible paths and locations in an organic fashion by using wandering versions of themselves. Say a zombieman, for example, has itself, and several "imaginary" zombiemen that wander randomly around it in a relatively close radius while trying to maintain line of sight with the real zombie (or being dropped when they break LOS and spawn a new one). They report if they have broken or gained line-of-sight to the player's last known (not real) position (itself marked by an "imaginary" player). They could also stop on health or ammo when they encounter it, if the zombie takes advantage of such things. The real zombie can then have a decision tree for which of these imaginary zombies it walks toward, depending on health, nearby friendlies, ammo, etc. A more "intelligent" enemy would have more imaginary versions of itself it can work with.
Another mitigating factor is that most enemies in Doom are not fast or strong enough in comparison to the player for any of this to make any difference. The player won't notice any additional subtly in most of the monsters unless they're significantly stronger or faster. For 90% of cases it's enough to set "afraid" on the monster when certain health ratios or range checks are met.