Yeah, this game works best if you are in a capable team. You don't even have to talk to others, it's enough if somebody tells everyone in chat what to do.
I'm having the most fun with my cruisers and destroyers. I hate it though, when I get one-shotted (or nearly one-shotted) across the map by some lucky battleship
Correct on both accounts: Your first point is correct that games go excellently if someone devises a strategy and has the entire team cooperate, and battleships or aircraft carriers are often the ones who bark those orders if anyone. They're the capital ships, after all! In terms of your second point, one of the developers said on the official forums once that they figured that destroyers and cruisers would be funner, and thus more popular, than the larger warships, as a way of keeping the capital ship population down at a reasonable level.
Basically, the stronger a ship CAN be, the harder it is to play.
For example, carriers have some absolutely incredible destructive potential, but they are at their absolute strongest if the carrier captain masters how to manually drop torpedoes and bombs (letting the game automatically place the attack can lead to easier-to-predict attacks), which is something that I'm still not confident enough to do against anything but stationary targets!
Battleships can rip smaller ships to shreds, but it's a class that's more strategy and planning than action and shooting, where you even need to decide when to use certain types of shell.
Cruisers are the jacks of all trades, which makes them easy to play.
Destroyers actually are a case where they're very fast, but still very hard to master, and thus have some seriously destructive potential if you are able to, as you said, dodge incoming shells.
To put it briefly, plenty of people can pop out some torpedoes, injure an enemy ship, and then die to the enemy's secondaries (I know I've one that plenty of times, and still do).
To explain in length on how someone can last longer as a destroyer (aside from the obvious "stay far away from the engagement," which is a legitimate strategy if you would rather become a hunter in the later stages of the battle, after the other destroyers are out of the picture):
It might be worthwhile to invest two skill points in the crew perk that gives you a small indicator if there's enemy fire going in your direction, to remind you to look around. The perk above it, the one-skill-point perk that lets you know when your ship has been spotted, is an indisputable must-have for destroyers, especially at high tiers. The best way I can describe high-tier destroyer play is that it's "Metal Gear Solid in a ship." You sneak into the front lines, deactivating your AA guns, using equipment, crew skills, or anything else you can use to minimize your detection range, getting up close to an enemy ship but not SO close that it destroys you with its secondaries, and then launching your extremely powerful torpedoes to cripple or sink them! And if you need to disappear from sight after you've been spotted, you can pop smoke to generate a highly conspicuous smoke cloud but disappear inside of it, or use speed to run away with the engine boost consumable (that makes you more visible in the process because your ship burns fuel in a dirtier way and thus produces thicker exhaust smoke while the consumable is in effect).
The biggest reason why I love World of Warships is the way that even with straightforward controls, this game is strategy on top of strategy on top of strategy!