"There are so many checks and balances that no one can be carried or screwed unfairly."
If your definition of fairness is limited to "applying the same rules to everyone the same way every time," then that might be true.
However, when the rules are structurally unfair, inequities can emerge despite the equitable application thereof.
Remember what Felix Frankfurter said: There is no greater inequality than the equal treatment of unequals. That is the Catch 22 the bean counters use to displace and dispose of warriors.
Rereading your 29 and 30 makes me believe you will not be convinced that the Army promotion system is fair, no matter what I say.
I don't know what you mean by "bean counters" when it comes to officer promotions. Promotion recommendations are made by boards of officers, randomly selected from throughout the force, who are senior to those being considered. Before those officers cast a single vote, each and every board member must be satisfied the system is fair - usually accomplished by a day or more of practice voting.
Board members come from varied backgrounds. Typically there are 15 board members. All branches are represented - combat arms, combat support and combat service support.
The file for each officer considered for promotion (school and command selection also) will have as a minimum; an ORB (Officer Record Brief), an official full length photo, and a complete Proficiency record that includes all OERs (Officer Efficiency Reports).
The board is divided into three panels of five each. Each panel votes each officer being considered.
Let's say there are 3000 Captains in the primary zone (PZ) of consideration and the Letter of Instruction, signed by the Sec Army, allows for 2000 to be recommended for promotion.
When the three panels have completed their voting there will be a 1-3000 ranking. The cut is made at number 2000. Usually it's not that easy because the curve will put a big hump right at 2000. The entire board may decide to re-vote x number below and above the cut. In the end, there may be an open discussion to determine who is above and who is below the cut. In other words, Captains Smith and Jones will never know how close they came to being on the other side of the cut.
The LOI also allows for a maximum number of secondary (below the) zone (BZ) recommendations. A previous separate board has already screened the secondary zone down to a manageable number of "water walkers." The board can recommend any number from zero to the maximum number allowed in the LOI. In any case the BZ recommendations do not take away from the PZ numbers.
Of course the board members are subjective, but I don't know how the system could be any more fair.