First off, even if you're looking in a very reductionistic manner at game balance, mechanical elements are still too diverse to be characterized independent of context. Is it better, for example, to spend your feat on Skill Focus or Weapon Focus? It depends. It depends on whether you are likely to be able to acquire a good version of the specific weapon. It depends on how many attack rolls you are likely to roll, how likely they are to hit, and on a variety of other factors related to the difficulty of combat. It depends on what skill the Skill focus is for, how often it is likely to be rolled, what the DCs are, how useful the skill is likely to be...and a lot more. Most of which is decided by the DM. In one campaign, Weapon Focus (Longsword) might be close to the best feat available. In another, Skill Focus (Spot) might rule the day. You cannot tell which feat is better just by looking at the rules, no matter how knowledgeable you are or how hard you look. There are only very rare cases where one particular option is unambiguously better than the other, usually in different publications that are not cross-referenced very well.
Even if we restrict ourselves to pure combat feats, would you rather have Power Attack or Weapon Focus? If we have two GM's, one who favour Giants (low AC and high HP for their CR) an the other likes incorporeal undead (high AC, low HP for their CR) the answer is likely different between the two campaigns. "Balance" has a lot of variables. Ranks in Swim? Are we playing a High Seas pirate game or a desert scenario. [And Iif I just say "Arabian Nights", do I mean Aladdin or Sinbad?]
Bottom line - I agree there's a lot of variables and "objectively balanced/unbalanced" is pretty tough to spot.
Of course you can. In a balanced campaign, one which features equal amounts of combat and exploration and interaction (the three pillars if you will) then neither feat will be measurably better than another. You will get pretty much equal traction out of either feat. If the game leans more heavily on combat, then weapon focus is likely better, in that specific situation, which is actually outside the baseline presumptions of the game in the first place.
So do you want Power Attack or Weapon Focus? Now we have to assume an equal mix of types of opponents as well. "Perfect balance" can exist only in a specific hypothetical campaign, and every campaign is different.
Clerics in 3e are easily better than monks. In virtually any situation and certainly over the course of a campaign, a cleric will shine far more than a monk. It attacks better, does more damage, has way more options and is better out of combat as well. There's nothing a monk can do that a cleric can't do better. Never minding Druids. There's a reason people talk about CoDzilla. And, if you don't believe me, we'll take two groups through any module you care to name - my group is 3 clerics and a druid, your group is 4 monks, and we'll see who gets further.
This seems like a "PvP" structure - it's every man for himself. Monks are synergestic characters. The Monk is a lot better at getting past that line of grunts to get to the spellcaster 50' back while the warriors take care of the grunts. They're mobile, so they can help the Rogue benefit from his sneak attack. The Monk also has an advantage if we throw a lot of encounters against him without opportunity for rest and prayer - he doesn't run out of spells that need to be replenished. That doesn't mean that the Monk can't stand a power-up even in Pathfinder, much less 3e where non-spellcasters in general are quite disadvantaged. Want real power? A balanced team that focuses on enhancing team, rather than individual, power.
Trying to whitewash balance issues by pushing it off onto individual DM's is the reason why so many games fail. Many DM's, particularly starting ones, don't have the experience to know how to fix the broken systems. So, you get someone like me, who is interested in the nuts and bolts of gaming systems, sitting down at different tables, and the DM throws up their hands crying, "Hussar is a bad powergamer, his character just steamrolled over my encounter" when all I've done is pull stuff straight out of the PHB. I mean, I mentioned one DM crying powergamer earlier, when my cleric had two levels of half-elemental. Yeah, I'm a powergamer for taking off class levels in something that granted me fire resistance and the ability to cast burning hands a couple of times a day. Ooooh...
Care to refer me to the PHB references for half-elementals? I'd say that's a very powerful ability if the GM is using a lot of encounters featuring fire damage, and an extremely weak one if fire damage rarely, if ever, is encountered. The more aed material, the greater the prospect for overpowered, or underpowered, combinations. The Cleric got a lot more attention from both WoTC and 3rd party sourcebooks, so he gained options quickly. Options that could be combined to added power. If there were as many feats relevant to unarmed combat as there are for spellcasting and undead turning, the Monk would have a lot more options.