Assuming no mods and no other relevant traits, taking a level of Triggerhappy boosts your volume of fire by 20% with a chaingun, 12.5% with a plasma gun. Taking a level of Finesse boosts your volume of fire (average number of rounds fired in any given length of time) by 11.11% for either chaingun or plasma gun, under the same conditions. Now Triggerhappy is one of the most desired traits for a chaingun-based character, and you have to take 2 levels of SoB to even be able to take levels of Triggerhappy, so it's asking a lot to ask that Finesse, which you can get at the very beginning of the game AND which unlocks two (more than any other single trait in the game) other traits, be as powerful as Triggerhappy. All the same, you can see that it's not out of the ballpark of Triggerhappy, in usefulness. Two levels of Finesse, which you need to get the (sometimes extremely important) trait Whizkid, increases your average volume of fire by 20% with weapons like chaingun and plasma rifle; as much as a level of Triggerhappy in the case of chaingun, and better than a level of Triggerhappy in the case of the plasma gun.
The most important situation for Finesse is certainly Angel of Marksmanship, not only for the sake of getting Whizkid to pump up your advanced pistol full of mods, but for its own sake. I don't want to crunch the numbers right now to give exact firing times, especially when someone like Kornel probably could work out those figures more easily than I could, but in Angel of Marksmanship, taking 3 levels of Son of a Gun and putting 2-3 speed mods on your advanced pistol will get you roughly 2 dualshots/second, while taking 2 levels of Finesse in addition will get it down to just under 3 dualshots/second--a very noticeable improvement. This is from memory, though, and maybe someone else can check to see exactly what the numbers are.
I DO agree with you that Finesse might be slightly underpowered, but not by much--dropping firing time by 15% instead of 10% might be a good idea but any more than that and I think Finesse would suddenly come alongside Eagle Eye as a "must-have" trait.