In Classic, Revised and Enhanced, the Submarine is an invaluable tool of any naval combat.
In Anniversary, they are a joke at best, a horrible waste of manufacturing time at the Hasbro plants at worse.
I used 10,000 submarines and 1 destroyer with 4,999 bombers (equivalent cost) for a reason. It demonstrates just how bad the submarine is. It’s akin to running a simulator over 10,000 identical battles to see if this one battle should go your way or not (like when you use Frood to find out the probably results.)
However, in this case, it is very simple to see that any major submarine investment is going to end up costing you a lot more than your opponent will lose going with a couple of destroyers and a large air investment.
You’ve mentioned that you can just keep your submarines out of range of your opponents destroyers. That’s great! But what, exactly, are your submarines doing then? They are not helping you win the war, they’re too busy running away! (Watch the movie Das Boot, that submarine did more for Germany in that movie than any submarine in Anniversary will likely do for you in the end.)
If you don’t run away, then your opponent can easily swoop in with a destroyer and a whole bunch of planes to sink a large number of your submarines for very minimal cost to himself. (Sure, if you have enough submarines he may only get one round, but in that one round he can still sink 1 submarine for every 2 aircraft attacking on average, maybe more once you factor in bombers and/or technologies. That group of submarines, no matter how many there are, can only sink the destroyer, you cannot sink more than that.)
All I am saying is, if you have a choice between submarines and anything else, including extra AA Guns, you may want to seriously consider the “anything else.” (Though, perhaps the submarine might be better than an extra AA Gun…they cost the same, but I can see a situation where the gun would be slightly worse than the submarine.)