The whole Idea is you only put your surface fleet out where you have friendly air superiority or at least contested air. That's the whole reason in multiplayer that the Central/Eastern Mediterranean is one of the most important places to fortify airbases on, whoever can get the most planes up for a naval battle will win the decisive battle. Italy typically wins central med, but UK wins eastern med, because Allies only have 2000 planes stationed in Malta while Axis has Sicily and multiple bases in Libya to contest air with. Eastern Med meanwhile has Cyprus and Alexandria if not Palestine to provide air support from.
The reason the naval meta exists in its current state is that it's better to have more ships than to have fewer ships, even if the few ships are individually more powerful. The cheaper you can make your ships, the more ships you will have. You don't need to have expensive AA guns or sacrifice attack for dp secondaries when friendly fighters stop all the naval bombers for you.
Also, 1940 destroyers have 50 hp, which means that it takes multiple hits to sink one unless the enemy targeting it has 50 light attack. the more ships you have, the less likely that ship is to be hit multiple times. The targeting formula is random and ships don't get focused down. Also take into account that a 1940 DD with engine 3 will be decently evasive, and your destroyers won't sink nearly as often as you seem to think they will. People have run the tests.
EDIT
More info on naval targeting and AA, the typical thing to do at game start is to refit all your starting battleships and battlecruisers to carry only AA guns, since naval bombers heavily prefer to target them and carriers before anything else. They have enough hp to sponge the naval bombers attacks while your CAs and DDs don't take many hits because they are not targeted as much.
You do realize that the OP is in a singleplayer game talking about playing Germany as a naval power, right? You're talking about a multiplayer battle in the Mediterranean. You're also talking about massing empty destroyers for a fight that is going to have rampant subs (either as minelayers or raiders, or both) where minelayers are going to cause massive penalties to ship movement (
80% speed loss; note that accuracy is reduced by ship speeds, so everything shot at these ships is going to hit). I also dislike people pulling the multiplayer and meta cards because it basically says that any opinion other than mine is wrong because some other people have gotten into a habit of all doing the same thing in our games because it seems to work.
For starters: the AI can be countered by far more strategies than just one. The AI is entirely willing to fight in places that are heavily mined, or that are in enemy air superiority (hence the frequent statements by veteran players that you can just bomb the AI into oblivion). Then there's the obvious factor that if most of your fleet has 0 AA while a few battleships have no light guns and max AA (and now are useless in fleet battles, and solely exist to get bombed...), then you can't move your fleet around safely without air superiority.
Then, in case you missed the irony here:
The reason the naval meta exists in its current state is that it's better to have more ships than to have fewer ships, even if the few ships are individually more powerful. The cheaper you can make your ships, the more ships you will have. You don't need to have expensive AA guns or sacrifice attack for dp secondaries when friendly fighters stop all the naval bombers for you.
This explanation of the "naval meta" fails to actually explain WHY at any point. It is a definition, not an explanation. I also like the logic that AA guns and DP secondaries are expensive, when you need fighters to actually shoot down the enemy bombers (fighters have an IC cost that's also pretty high, of between 22 and 28; they also all cost fuel, about 170 per 100 fighters compared to about 32 per light cruiser).
Resource costs are also an obvious problem. If someone wants a major fleet, then higher-tech ships (you mention 1940 destroyers) are going to increasingly cost steel, and later chromium, in large amounts. Germany (the nation in the OP's case) can afford steel costs at first, but has to purchase chromium and will eventually start running out of steel (and going closed economy hurts all your European allies that are likely buying all of your spare steel, although its fair that some players don't care about that). Refitting ships and repairing ships, by comparison, costs no steel. If I suffer heavy damage to 8 light cruisers and you lose 24 destroyers, you need to spend 2-4 steel per destroyer replacing them, while I need to spend 0 steel repairing my CLs. Refitting existing cruisers as time goes on is also pretty cheap, meaning that putting DP secondaries on existing ships in 1940 also costs 0 steel. This is rather amazingly-important since infantry equipment, artillery, and tanks are going to consume your steel stockpile rapidly (even if you focus mostly on aircraft).
Then the last bit: DP secondaries as an "expensive" sacrifice compared to CL-2 turrets:
CL-2 Gun: 275 cost, 5 damage, 7 piercing, -4% speed
DP Secondaries: 290 cost, 4.5 damage, 8 piercing, -3% speed, 3 anti-air
In other words, these actually slow ships down LESS than CL turrets, do almost the same damage, have better piercing (thus more damage against armored targets), and that's all without taking into account that they just happen to also carry 3 AA. CL-3 guns are a bit better (6 attack 8 piercing 300 cost), but also cost 1 steel PER GUN (meaning that 5 CL turrets on a heavy cruiser costs 5 steel more than a light cruiser, plus 1 steel for the heavy cruiser turret, for only 30% damage increase). The tech also takes longer to research than DP secondaries, and doesn't benefit capital ships (besides CAs). Steel economy to me is vastly more important in the late game than extra firepower on my cruisers.
Lastly, the mine issue. If you want to pull the meta card, then mining the crap out of your coastline and the English Channel with subs is going to give you up to an 80% penalty to enemy ship speeds, which means your point about needing to score 2 hits to sink a DD is now actually that every 2 light cruisers are going to sink a destroyer every single shot. By comparison, the DDs themselves are doing about 80% reduced damage due to armor and can't score critical hits, while the heavy cruisers only get 40% damage boost while screened and also fail to get any critical hits (8 armor isn't enough for much damage mitigation though). If 5 light cruisers engage a cost-effective enemy squadron, you're talking about only 2 heavy cruisers and 20 empty destroyers, which actually represent LESS light attack (even after screening bonuses) than the opposing fleet; the 20 DDs just represent about 40 shots from the CLs (and after 13 kills, the CAs are no longer screened), which means that they need about 8 hours in-game to sink the entire enemy destroyer force. That's how long the two CAs have to cripple the light cruisers, and while that is possible (if they ALSO mined the English channel), you need to sink the force within a single day or you are going to lose (since if two CLs retreat, I still have 3 CLs fighting that can sink another 36 destroyers in 12 hours).
Then there's the minor bit that even submarines can tear up that fleet pretty easily, since they'll be faster if the waters are friendly (and thus not mined by enemy ships). a full fleet of subs would kill 31 destroyers more-or-less instantaneously in those circumstances, then just need to survive 4 rounds to kill the entire remainder of the fleet; and 31 subs is a pretty small force for 1940.