care to test these IC for IC?
No, but I will theory craft it.
These CL3, coastal designer, armour 3, engine 3, and a single lowest tier CL gun turret (for bonus HP, least impact on speed and lowest cost) 2636.25 IC. A DD2 with coastal, engine 2 and lowest tier DD gun is only going to cost 532.5 IC. So you could get nearly 5x as many DD for the same IC cost, while the CL also costs 1 extra steel and a chromium per yard.
The CL has 154 HP and 10 armour. Piercing will range from 7 up to 8.8, which means a damage multi of -27%, or -10.8%. This increases its EHP up to 211 at best, 173 at worst. The DD only has 40 HP. An attack that would perfectly 1-shot the DD would take 5 or 6 shots against the CL, but having slightly more damage than is enough to 1-shot DD shifts that down 1 to 4 or 5 shots. As damage continues to climb, the DD doesn't get sunk any faster, but the cruisers do.
The CL seems to have a visibility of 13.5 and a speed of 45.628, which results in a profile of ~29.5. DD has 10 visi, 43.23 speed, profile of 23.15~. This means that against light guns, there is about a 6% chance to hit the CL, (about 16.6 attacks to land a hit) while the DD is about 3.7% chance to get hit (nearly 27 attacks to get a hit).
532.5 IC divided by 27 attacks, is ~19.72 IC spent per enemy attack absorbed for the DD. The CL takes its 2636.25 IC cost and the 16.6 attacks per hit, x6 for the hits it can take (99.6) and we get ~26.5. The CL is almost 33% more expensive per attack absorbed, in what is essentially the best case scenario for the CL. If we went x5 or x4 due to increases in enemy damage/piercing, its 31 or 39 which is massively more expensive.
The fuel costs are basically the same, 40 for the CL, 40 for 5 of those destroyers. The 5 DD also technically have more light attack, but it has worse piercing and is distributed across a greater number of ships so it is less effective. More of the DD is also going to drag down more of your range.
Note that this does not account for the ways that admiral/other defense boosts will boost armour and reduce damage, because that gets more complicated and even as noted here, the CL is already losing by a pretty big lead. I'm also not accounting for the CLs ability to take multiple hits, and therefore potentially absorb more total damage before a ship is sunk and your screening efficiency is affected. 35 of these cruisers at x6 hits could take 175 hits before a cruiser is sunk and still have 35 ships screening, while for 175 of these DD that would be 175 sunk (actually only 108 with hit rate) which leaves 0 (67) ships screening.
If we want screen ships for the purpose of giving the capitals their screen bonuses for as long as possible, it is difficult to argue against the roach DD. Only when you want to start boosting range, or trying to skew the larger fleet penalty in your favour, do CLs start to enter consideration, and it is always at cost. Who would have thought that spending more on your navy would make it better. But navy is always the sort of thing you want to spend as little as possible on, so cost-effectiveness is practically king and is why the roach DD is so prevalent.