Enjoyed reading all the thoughts thus far. There are too many that I want to comment on, so take this as my consideration of the card and the conversation.
1) This is obvious, but the cost of the cards is 4 + attack effectiveness, defense effectiveness, or effectiveness through flexibility, all of which are bestowed in the officer slot.
1a)This means that on offense, you are betting that an extra activation will net you more than, for example, restricting token usage (Intel Officer). On defense, you are betting that the extra activation will net you more than such things as dice manipulation or hit negation (Lando/Derlin). However, most commonly, you are betting that activations will gain you more than flexibility that is often provided in dial/token management but can also offer a number of other benefits.
1b) An example of the opportunity cost is that while you may gain an activation and thereby be able to shoot at a ship you are otherwise unable to shoot, you also may lose the ability to speed away or maneuver to better get a double arc.
2) This card is a wager. If your opponent takes it, you have essentially canceled one another out. If your opponent has a much greater number of flotillas and is, therefore, able to simply activate another flotilla in response to your large ship, then you gain much less than if they must activate a more expensive ship into your area of attack. However, it can also mean the difference between getting no shot AND being shot at on the one hand or not being shot AND getting to shoot on the other.
3) All of this means that, IMO, this cards does not directly help 1+4 type fleets directly. It does make one of the activations cheaper or add another activation at a cheap price (4 points plus less effective power attack), but you already were doing that. Of course, we then must ask who it helps and who it hurts.
3a) This does significantly not hurt 1+x lists when the 1 is a large ship. They are likely to have enough activations that Mon Cal or ISD still gets its attack. They may lose the effectiveness of one activation, but more often than not that is a flotilla in these lists.
3b) This hurts MSU lists that rely on a number of smaller attacks but do not have a single heavy lifter. Goldfish lists or Raider/Arquitan lists lose an attack on a large ship and lose the ability for one ship to avoid getting shot at...per turn. They don't have the benefit of throwing away another flotillas activation because they rely on every activation making a small attack.
3c) This hurts 1+4 or 2+3 lists in which the heavy hitting ship is not a large base. This would include ships with strong attacks in small ships (Demo or MC30s for example) or in bomber lists (at least those which don't rely on a large based squadron pusher). Essentially, they must consider whether or not to add another flotilla. While this might cancel out Strategic Adviser, it costs 18-23 points bare. That is a significant cost, especially when even the possibility of this card, rather than its actuality, in an opponents list might force those 18-23 points.
Conclusion: In essence, this card forces 1+4 (non large base)/2+3 lists to double down and purchase another flotilla or risk out activation/losing first-last.
Edit: Please critique and nuance this as these are initial thoughts. I hope to revise and more clearly formulate them as we converse.