Acc will effect your performance far more than Atk until you're capped out on it. If you're already hitting 95% Acc (the cap), then obviously you are overkilling on acc and need to start worrying about Atk/STR. But until that point, you'll do far better DoT with a full Acc build. Hitting 95% of the time for 50 is better than hitting 80% of the time for 60. Honestly, many players won't have access to many of the better Acc gears (Woodsmans/Snipers, PCC). Without these, you will really need to focus more on the Acc gear available to you, which isn't much.

You can't really go too all out on the acc, just because it's not available on every slot. The only time I would consider switching an acc piece for an Atk piece is if the Atk piece had a significant amount of Atk (Spike Finger Gauntlets > Battle Gloves: 12 Atk > 3 Acc). The only other slot where I can think of this being a major issue is with Swordbelt vs Lifebelt.

You can put Acc on every slot you have and still have more than enough slots that have no Acc pieces to fill in with some Atk/STR.