Part 1 - Too long for one response x.x, sorry!
The problem with Banner of Command is that it serves no purpose to players. In its current state of being Banner of Command is really just a toy for players to mess around with and ultimate adds little actual benefit to players. Let's take a quick look at the stats.
Banner of Command provides:
40 AP
30 Armor
10% CDR
10 HP/5
2360 Gold
Let's compare it to
Seekers Armguard:
20(35) AP
30(45) Armor
1160 Gold
Picking up Seekers Armguard gives up more armor after a few creep waves and almost the same AP, but that also leaves us with 1200 extra gold to spend. With that extra 1200 gold we could buy several items that would push us far above the base stats of Banner of Command.
Codex - 820G
30 AP
10% CDR
Emblem of Valor - 650G
20 Armor
7 HP/5
Hextech Revolver - 1200G
40 AP
12% Spell Vamp (Generally providing more regen than Banners HP/5)
Or one could just save up for a Needlessly Large Rod to build into Zhonya's for 400G more than Banner.
Banner of Command has comparatively weak base stats and bad defensive timing compared to the Seeker's Armguard at less than half the cost. On top of this, Banner of Command is a fully upgraded item, taking up a slot with very sub-par base stats. So, seeing that Banner of Commands gold cost is not within its base stats, there is a massive amount of weight being applied to both it's passive and active. Lets take a look at them and why they are ineffective in their current state.
Banner of Command Passive -
10 HP/5
15% Damage to Minions
Let's assume you have a full creep wave including a siege minion. And we'll place it at the 21 minute mark for creep damage calculations.
Combined Creep Damage - 3 Melee, 3 Ranged, 1 Siege
229 AD Damage
195 AD Damage to Champions
344 AD Damage to Turrets
+Banner of Command Passive
+34 263 AD Damage
+29 224 AD Damage to Champions
+51 395 AD Damage to Turrets
If we assume turrets are running around 70 armor and Champions around 100, then we get.
+15 AD Damage to Champions
+30 AD Damage to Turrets
These numbers aren't too bad, providing close to the worth of a Pickaxe to player in an optimal situation. However, very rarely does this occur. Creeps are easy to kill, often at this point getting instantly killed by AP mid or at least close to it. With each creep that dies, the value of this passive goes down and down. It's greatest use would be against a tower, during a split push, when left alone. In this case, that passive of Banner of Command would in handy. We can estimate that over the course of a full wave only being attacked by the tower, that the extra damage would be somewhere around 150-250 to a tower, a solid amount. Against champions this is much harder to determine, but we can assume it will be much less significant as the uptime of minions attacking creeps is normally pretty low and hard to predict outside of the early laning phase. Even if we consider it to contribute a healthy 100 damage (that's 6-7 attacks from each creep in the wave), the value of that passive compared to a pickaxe pickup (which would contribute guaranteed damage) is far far less.
As we can see, the value of Banner of Command's passive is fairly low, situation dependent, and unreliable. Personally, I'd value it around 200 gold, but that's just my opinion. So what accounts for the high Gold Cost of Banner compared to other similar items. It's Active. Let's take a look at it.
