Not exactly a senseless rule, but a confusing choice of words: armour proficiency.
In every single instance "proficiency" means adding your level-dependent proficiency bonus to the relevant d20 check. Weapon, skill, tool, save proficiencies... If you have it, add your +2 to +6 to d20+ability modifier. Except for armours, that is. I'm willing to bet there's a not insignificant number of people adding proficiency modifiers to their AC. A simple change in wording would have been enough: armour mastery, for example.
As for tools/skills discussion, I'm of the opinion that the system itself is more or less OK. What tends to confuse people is that the rules for these closely-related systems are split into two different chapters. Speaking for me personally, as an experienced gamer, I had some initial problems figuring them out and had to carefully re-read Tools section of the Equipment chapter before I could fully grasp the intent.
I'd like to see two ease-of-use changes. One, don't call both tools and non-tools "kits". It's mighty confusing. Two, consider moving Tools section from Equipment chapter into Using ability scores chapter, right after Skills. Maybe it isn't that elegant (tools are equipment, after all), but I really feel both skills and tools should be discussed side by side.