I think Support Doctrine is already borderline too strong as it is, being able to choose which skills you get would make it way overpowered.
The biggest benefit of granting those skills is that they are unlimited; if you have 30 ships without officers, it's granting 30 Combat Endurance, Helmsmanship, and Damage Control. I always take Combat Endurance on all officers anyway, and I use Helmsmanship on them 90% of the time as well. So it's granting two skills that I'd be taking on officers anyway.
Officers are strong, but they also have a significant cost: they decrease your XP bonus. A level 6 officer counts as 30 DP for the purposes of the XP bonus, so if you have 10 level 6 officers with your 300-DP fleet, those officers just cut your XP gain in half. I usually plan for fleets to run at around 400-500% XP bonus against [REDACTED] fleets (depending on if the fleet is built for single, double, or triple [REDACTED] fleets), so whether or not to use Support Doctrine or officers is a crucial decision point. Support Doctrine means I get to put about 25% more ships on the field, which also means 25% more DP cost for the XP bonus (the DP reduction doesn't affect the XP bonus), versus officers where each officer will cost me 26.25 DP (if level 5) or 30 DP (if level 6) to my total DP for XP bonus purposes.
For that decision point, *if* I use Support Doctrine, since I almost always take Combat Endurance and Helmsmanship anyway, then it's really a matter of whether or not the other 3 or 4 skills for an officer is going to worth the DP cost for XP bonus purposes. For some ships, it clearly does. For example, an officered Gryphon does around 75% more overall damage throughout the battle as an unofficered (with Support Doctrine) Gryphon, with the biggest contributor being Missile Spec. Hyperions also benefit a lot from officers. For others, even though officers do definitely help, it may not to the same extent, in which case Support Doctrine may be better.
So in that sense I think both Amoebka and BigBrainEnergy are correct: Support Doctrine can be used to help unofficered big ships, or unofficered small ships. It really depends on the particular ships (their power "ceiling" when using officers, versus their power "floor" when not) and the use case scenario. Each way of using it can be successful.
In fact, destroyers and frigates tend to have better savings because of the way rounding works. 8 DP Shrike becomes 6 DP (25% discount), 22 DP Eagle becomes 18 DP (18% discount).
It really depends on the ships. Any ships that have DP of 3, 4, 8, 9, 13, 14, 18, 19 etc. get better savings. Any ships that have DP of 1, 2, 6, 7, 11, 12, 16, 17 etc. get less savings. Smaller ships do get proportionally better or worse savings though (so that uh Hound becomes 2 instead of 3 OP). But for example, Falcon XIV (becomes 11 instead of 14 DP) and Apogee (becomes 14 instead of 18 DP) are some cruisers who get more benefit from it than average.