+Attack Refines?

Yeah, pretty much. The might increase is always the least significant when compared to other options. What baffles me even more is when I see tomes having the atk upgrade, which adds 1(!) point of atk when compared to other refines. Even the heaviest blade can't justify using that.

A lot of attack refines are on units that have effective damage because it actually scales pretty well with each additional point. It just helps ensure you can kill all those pesky armors that are running around, as an example.

That's one rational reason at least.

I use attack refine on my Hawkeye because I prefer his speed to be lower and his physical and magical bulk are both in the "good enough" range. His attack is already good but the atk refine gives him just a little more player phase potency, and opens him up for opportunistic "clean up" kills on green and red targets that he would normally need to avoid.

I think that the Atk-refine is going to be much more useful on units that can double regardless of Spd--mainly, the Bold Fighter Armor units. Since the point is to take care of the enemy in the same round of combat that your unit initiates, Atk becomes more important than any of the other stats. Spd does nothing for your ability to double (because you are already doubling), Def and Res are unnecessary if the enemy is dead by the end of combat. I also think that units that can avoid most follow-up attacks, like the Wary Fighter Armor, can run Atk-refine effectively because they are quite capable of tanking the one strong hit, then hit back harder.

Spd-refine is more important if you want your unit to either double to kill (because Atk-refine might not be enough to secure kills), or avoid as many follow-up attacks as possible. Def- and Res-refine are more useful for lasting multiple rounds of combat against a particular type of unit and/or rounding out both Physical and Magic bulk. I guess that most units would fall into this category rather than the Bold Fighter / Wary Fighter Armor category, or something similar, hence why most people would recommend against the Atk-refine in favor of something else.

It would really depend on the rest of the set.

Attack refines are great on a DC vantage set as that 2 points of attack can mean the difference of the enemy getting an attack in or not. Anything other than that and yeah you are probably more likely to benefit greater from a different refine.

I'm more or less with you on this one unless it's some kind of all-in attack build. If it's a slow unit I tend to look for a defensive stat increase (and build accordingly); if it's a fast unit I'm likely to take spd. The only time I've suggested an atk refine completely from me is the vantage Nowi build, which fits the all-in attack description: +atk IV, lightning breath +atk, brazen atk/def (or atk/res), vantage, res smoke, atk+3 (or deflect melee). Before Breath of Fog was introduced, this was also a reasonable setup for A.Tiki. (It still has some merit, because Breath of Fog+eff = 19 atk while lightning breath +atk + brazen atk/def = 21 atk, and you save 250 dew - 200 that you didn't spend, and 50 stones that you spent instead.) Very one-dimensional, but it should work pretty well with 61 magical damage potentially compounded on res smoke. I don't think any refine has a significant advantage over atk here; in fact, the others are probably inferior because she probably won't avoid any additional doubles with a spd refine, whereas a OHKO does prevent a double (or perhaps getting hit at all).

The only other build I can think of that might use an atk refine well is slaying + glimmer on a massive atk stat like Effie's. Even there I would probably prefer def or res and try to get the atk from a buff instead. I can squeeze out more stats that way.

I took on a 70+ atk visible stat challenge from reddit once, so I did it.