360 Degree Vision
From the question:
To me, this is overreaching, since a character can’t be aware and targeting 360 degrees, any creature, but only if it’s “hostile”, etc..
Another example, in a room with multiple doors, east, west, south, says “I attack anything entering the room.” But, can they cover all three at once?
It's entirely reasonable and within the rules for the character to be aware of enemies from all directions, given certain conditions. PHB 177 (section on "Hiding") says:
In combat, most creatures stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you. However, under certain circumstances, the Dungeon Master might allow you to stay hidden as you approach a creature that is distracted, allowing you to gain advantage on an attack before you are seen. [Emphasis added]
This would absolutely extend to a state of active readiness (like maintaining watch with bow drawn or spell prepared). This means that if an enemy approaches openly from any direction, your warlock would be able to spot them. The only time they wouldn't automatically spot an enemy would be if they had some way to approach undetected (e.g. invisibility or some rubble to hide behind), at which point it would be a stealth vs perception contest to see if they are detected.
Action Economy & Surprise
There's one other potential hiccup in the way this works, and it can be kind of situational so I'd like to cover it in detail. For the exact rules, see page 189 of the PHB.
The biggest factor is to determine who is surprised. If the player is actively watching for enemies and has a readied action, but some goblins wander into the room without actively searching for enemies, it would be most reasonable to rule that the goblins are surprised. This would mean that the goblins take no actions on their first round of combat, effectively giving the warlock (and any other players with actions ready to go) a free attack at the start of the fight. This does not mean that the Warlock gets to use his reaction to cast the readied spell, and then follow with a normal action during surprise round. He only gets an action as usual.
However, if the Goblins have heard noises and are suspicious someone is there, are actively on guard and paying attention with weapons drawn, or are otherwise aware of the possibility of combat, the situation is different. Unless the players are hiding somehow (and successfully beat the Goblin's perception checks), I would not rule that the goblins are surprised at the start of combat. In that case, the Warlock was ready to fight as soon as he saw enemies, but so were the Goblins. At that point it comes down to who is quicker on the draw (represented by initiative checks). If the goblins have arrows nocked and he has a spell ready to go when they walk into the room, they would both fire at essentially the same time (fire at the same round, with who shoots first determined by initiative).