A lot of the complaints about the current FITREP system seem to stem from a misunderstanding of how it works, so it seems to me that is the biggest flaw in the current system - it is not easy or intuitive to understand and not every CO/XO is good at explaining it. It's like the tax code - it's sensible as long as you can understand all of the nuances contained within.
I had a DH who phrased this well: "Work not seen is work not done."
'Work not seen is work not done' is a pretty cynical way of saying 'you should focus most of your efforts on initiatives that are important to the command.' Not because you are brown-nosing, but because if it's high enough on the list of stuff that it gets the attention of an O-5 or O-6 then it must be important and you certainly should put it high on your priority list as an O-2 - O-4. But if you want to take the approach of 'nah, that's stupid, I'm instead going to be the best [insert low-level item that has no command visibility] instead of delegating that to someone,' you shouldn't be surprised when your boss is frustrated that you can't/won't manage command initiatives and ranks you accordingly.
They reward visibility of performance over actual performance.
I don't think that's true, but as everyone here knows, communication is an important trait of being a leader. If you can't effectively communicate what you are doing to improve a division/department or support a command initiative as a DIVO/DH, then how is the CO going to think you can effectively communicate to a Commodore or Admiral about how your ship is ready to support its mission? The fact that people who are not good at effectively communicating are left by the wayside is a feature, not a bug, of the current system.
As for promoting dipshits vs. superstars, I'd be interested in how much the opinion of who constitutes a good officer or CPO differs among seniors vs. subordinates. Sometimes you get both, but some of the best military leaders in history were not well-liked by the officers or men who worked for them.
Some other gripes from the Navy times article:
-Seniority is valued over performance. When you consider that FITREPs are a recommendation for promotion/screening and not a report card, this makes quite a bit of sense. Who is more ready to be an XO, an average DH with 2 1/2 years of experience or the above average DH who showed up 6 months ago? It doesn't matter if you hit the ground running, you don't yet have the necessary experience and maturity in your current billet to move onto the next career milestone, and so your recommendation for advancement will reflect that. Where the current system gets muddy is when you have a gaggle of LTs who are all on similar timing, and someone who performs well early gets leaped by someone who performs better later in their tour. Since putting that on a FITREP to the early high performer can be detrimental, that can lead to a sticky situation if both are guys you want to keep around. There may be some 'tricks' to managing this, but see my first point about the nuances within the current FITREP system being its main flaw.
-The ranking system doesn't allow a CO to communicate a hot-running wardroom or a wardroom full of mouth breathers: I would wager that the times this happens is very, very rare. It's natural to think the guys you work with on a daily basis are the best group in the Navy, but I would imagine that's based more on emotions than any objective criteria. Every officer in the Navy has met the screening criteria, so from a "Big Navy" perspective they all have the necessary tools to be developed into effective leaders. In the case where a ship does have an exceptionally talented group of officers, there will be some objective evidence of that reflected on the FITREP - awards, inspection results, operational employment, etc.