A lot has to do with targeting priority. Heavy guns and naval bombers(and light guns for that matter) go for the most visible ships in the targeted row. So if you have some starting battleships (refit to be filled to the brim with AA guns) all your CAs will barely be targeted. Likewise, CLs will be targeted before DDs. Since screens only attack other screens, your CAs are basically invulnerable. If you have tons and tons of shitty destroyers, the damage gets spread out a lot. if you roll 50 attacks against 50 ships, there's a pretty good chance that some ships take multiple hits and go down. But 50 attacks against 200 ships, you're more likely to see a few ships die but most only take light damage, even in a big battle. The high screen ratio also protects your CAs and other capitals from being attacked by torpedoes as they use all their light attack to decimate the opposing screen line. Once the opposing screen line is dead, heavier ships will eventually be picked apart by critical hits from all the cheap tin can destroyers and CAs, even if their armor is not pierced.
EDIT: And the reason no one puts armor on the heavy cruisers is because CA armor is useless against heavy guns on anything bigger than a CA, does nothing against light attack because the capital line won't be taking hits from light attack, slows down the ship which makes it easier to hit, and is more expensive, meaning you can build fewer CAs.