If you read the following paragraph in the PHB after the section you mentioned on turn order (pg. 189) you'll see it says:

If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a reaction until that turn ends.

On top of that, it's important to note that

A round represents about 6 seconds in the game world. (PHB 189)

So in this case it translates to:

1. Warrior takes his turn. He can choose to ready an action here to use his reaction later to attack Elf2 when the Rogue attacks Elf1. Note that the Warrior can move into range if necessary and will not affect surprise as surprise is determined before turns are taken.
2. Elf2 does nothing and is no longer surprised. He can now take reactions. If the rogue attacks him there are no bonuses related to surprise added to that attack.
3. Rogue takes his turn. When the Rogue attacks Elf1, the Warrior uses his readied action.
4. Elf1 does nothing and is no longer surprised. He can now take reactions.
5. Combat proceeds as normal using the same initiative order. (Readying an action does not change initiative order so it will still be Warrior, Elf2, Rogue, then Elf1)

Thinking like a monster

There's no question: focus fire is a good idea. No matter how you look at it, the mathematics are in your favor if you try to injure one enemy until it is down, and then move on to another. Once you realize this, it may seem like you either have to use this tactic, or be completely unrealistic to what an enemy would do. But there are a few rationales for why a group of enemies would fail to use focus fire. And not all these are "screw what's rational: I want my PCs to survive." It can sometimes be more realistic to have your monsters avoid focus fire. Here are a few possible reasons they might.

1. They are used to weaker enemies

Many "evil" creatures prey on creatures far weaker than themselves preferentially. A squad of goblins might be used to attacking only the sick, the weak, or the unarmed and unarmored: merchant families, or innocent homesteaders. Most importantly, they may be used to enemies that go down in one hit. In a situation like that, it's actually disadvantageous for the goblins to all aim at the same enemy: their first salvo might end up hitting an enemy with five arrows when one would have killed him, and leaving other targets unscathed. By spreading out their attacks, they ensure that they drop the maximum possible number of enemies in the first round, ensuring no one escapes and leads to a messy and lengthy hunt. Perhaps these monsters default to such tactics, only realizing part way into the combat that these opponents do not fall so easily.

2. Enemies act at the same time, but don't think as one

Trained adventurers can act in groups as a seamless unit: adapting their tactics to those of their allies almost instantly. But lesser enemies (again, let's default to goblins as an example) fight without discipline. Perhaps all the goblins do think that they should focus fire: concentrating on a single enemy. But each goblin might have a different opinion on which enemy that should be. Three of them might shout conflicting orders at the same time ("Shoot the human with the bow!" "Shoot the shiny dwarf!" "Shoot the elf who set me on fire!"), and different goblins might follow different orders. If anything, the fact that these enemies are all acting on the same initiative might give more justification for them being confused as to what the other goblins are doing: they act almost simultaneously, and don't have time to notice their companions' actions, or to coordinate their efforts.

3. Monsters are selfish and dumb

Naturally, this one depends on the particular enemies you're fighting. Some enemies might be inclined to focus fire in spite of low Intelligence scores due to their natural instincts to focus on one weakened enemy at a time (like wolves). But generally speaking, some monsters aren't that smart. Even some very intelligent enemies (like vampires) might not be used to fighting in a group, and might simply fight using their own priorities, rather than trying to use teamwork. Some monsters fight based more using rage and bloodlust than tactics and intelligence: even if those monsters are intelligent enough to plan and think tactically, they may abandon these plans in the heat of battle, and attack only the creatures that hurt them, or the ones that look smallest, or the ones that look like they have the most valuable equipment. The three monsters who were hit by a fireball might all aim at the wizard, but the four who weren't might focus on the Paladin to loot his shiny armor. Bottom line, monsters' motivations aren't always to make the smartest move: sometimes it's to make a move that satisfies some baser instinct.

4. Monsters don't know what Hit Points are

This is a big one (and is kind of a variation on point #1). "Rationally", every arrow that a monster fires is an arrow they expect to find their enemy's heart, and drop them dead, regardless of whether it is the first arrow fired at an enemy or the 50th. Monsters don't know they are in a game, and that it is statistically impossible for a goblin's first arrow to drop a level 5 raging Barbarian. The monsters may spread their attacks around because they expect that each attack will kill an enemy. They don't know that "1 hit point" is a status an enemy can reach: they just know they hurt their opponents until they go down.

Likewise, we (as DMs) know what the best tactics are against this particular party, but the monsters may not. For example, enemies might not think to keep themselves spread out enough so that only two of them are in a Fireball radius at a time: why would they if they've never seen these enemies (or maybe any others) use Fireball? Similarly, it may not be particularly obvious to the monsters which creatures have lower max HP and which don't (note that HP often tracks stamina and drive as much as physical damage or resilience). Thus, they may make decisions that you, as a DM who knows everyone's stats and abilities, know is a bad idea: but it's not unrealistic or irrational for them to behave this way, because they don't have access to your information.

But sometimes... focus fire is the way to go

Note that all of these reasons (other than #4) are conditional. There may be monsters who are smart and/or great at using teamwork: they may target the weakest enemy like a pack of wolves picking off the weakest member of a herd. Focus fire can often be exactly the sort of tactic your monsters should be using, in which case, go for it! This can indicate that these enemies are particularly well trained, disciplined, or simply dangerous.

When the right tactic is empirically obvious to us as DMs, it can be hard to have our intelligent creatures behave in a tactically unsound way, while we strive to make their thinking realistic. But it's worth remembering that realistic thinking can be exactly the sort of thing that would lead to bad tactics. After all, people (and monsters) make bad decisions all the time.