Pirates being reckless is kind of a "pirate" thing to do. 
Is this true? Real pirates want to make money, not commit suicide. There's obviously some potential for 'desperation' attacks from small pirates down on their luck, but that doesn't really apply to huge armadas IMO.
FP may be hidden but the results are axiomatic: big fleets will chase same-size or smaller fleets. Likewise, bounty/pirate fleets almost always engage the player unless there is a huge disparity in FP. There might be some wiggle-room when two fleets appear to be roughly equivalent but I (anecdotally) don't see large hostile fleets running from medium-sized fleets filled with officers. I don't believe this is the OP's suggestion but the game would have to be clear as to why this is happening when chase behavior usually runs contrary to this.
I think the motivating issue is suicidal small fleets not, cowardly big fleets (which aren't really an issue because they are usually slow enough to catch regardless of if they run). The real problem is just that 'big' and 'small' are subjective (really should be more powerful and less powerful), but the AI needs to assign a number to those concepts to make decisions based on them. Fleet points are an attempt at assigning this number, and the suggestion is just to add more nuance to how the number is assigned to better represent the true strength of the fleet. I think we agree that the AI should generally run from fights they would lose and chase fights they would win. The OP is just suggesting that they fail to do that because they aren't accurately assessing whether or not they would win because they are missing important information about officers. I'm actually not sure if that is true, but regardless, I think fleets should be a bit more rational.
If I may ask for clarification, the end-result of the suggestion was so that the player isn't bogged down my battles that no longer pose any challenge? If the FP disparity is great enough, regardless of the hostile fleet's recklessness, why not give the option to auto-resolve?
It's definitely partially an issue of annoying battles/time wasting, but also just an issue of consistency. Why are these fleets behaving completely irrationally (sometimes)? I believe it is often referred to as the 'zombie hoard' of pirates. Hopefully the addition of new threats to the player in end game will allow pirates to not take this role in the game anymore and be more like actual pirates (opportunists looking to make some money rather than zealots dying for the cause of total anarchy). I think it's also somewhat important for the new player experience. One way a player understands their own fleet power is by the AI behavior. If a fleet is chasing you, you might gather that it has a good chance of winning, and if a fleet is running away, you might assume you have a good chance of winning, so I think it's important to try and achieve that to be consistent with the players expectations of how the enemy should behave.
I think the place I have personally notice issues is when I am somewhere in the late mid-game (strong cruisers transitioning to capitals). At that point I generally have many high level officers and my own skills as well as high quality ships and outfits. I would say that by that point, I can kill pretty much any pirate fleet because my ship and officer quality is so high, but the pirate fleets with a few atlas MK IIs still think they can take me resulting in a slaughter. Maybe it's more an issue of the AI over valuing the low quality pirate capitals (or those ships being too weak). Once I get a late game death stack, pirates usually run, although sometimes the biggest one still chase me which makes no sense.