Eagle with level 20 officer can solo some officer-less capitals (I mean proper ones, not Atlas mk2). And you get almost 2 instead of each Conquest, exactly 2 instead of Odyssey, etc.
With battle size 500 (max default) and 10 officers there is no strict need to use many larger ships. Maybe 1 capital under AI control and 1 for player.
What I like about Eagles is that they are very simple to use, both for player/AI and efficient. I think AI is least error-prone with Eagles compared to any other direct combat ships.
I find that 2 Astrals on bombing duty is more efficient than 1. You need a critical mass of bombers to accomplish anything with them and I find that 2 Astrals gives that critical mass. The Odyssey can solo a freaking Paragon, it's arguably the best ship ton for ton in the game being (much) faster than the Eagle with more firepower than the Dominator.
Eagles, like Auroras, don't really do anything at all. A mass of enemy Eagles is something of a minor threat, but one or two allied Eagles is at-best a distraction. They can MAYBE kill Destroyers, but the capitals all kill destroyers in seconds so that's never an issue. Tempests make a pretty decent distraction anyway, and unlike Eagles they don't tend to get surrounded and murdered.
Every ship in my fleet uses a level 20 officer. There's a reason I have exactly 11 ships. I do my testing with either officers or player skills, so that's another reason I expect every ship to punch above its weight in sim or else consider it trash, sim enemies have no officer stats. Sim ships also use default loadouts which have tons of wasted OP and garbage flux stats. Basically consider every Sim ship to be one weight class lower than it actually is, while every officer player ship is one weight class higher. Aurora vs Sim Eagle is therefor a capital vs destroyer battle in practice, and the Aurora manages to not win quickly enough so into the trash it goes.