Meh. I think the ultimate reason for not allowing improvement in them is niche protection for Thief type classes. I missed that they are actually gained from Adventuring, although spotting traps and secret doors makes sense. I'd certainly question hear noise, though, as that's the same chance for pretty much anything to hear noise (see Surprise and Sneaking). There are other things on that list that have identical odds for anyone (i.e., monster, NPC, etc.), whether or not they have Adventuring.
Also, I think the main purpose of Adventuring is simply to remove any arguments over all the standard things that adventurers try and do (Swim the river? Well, do you have swimming? Tie up the Goblin? Well, do you have rope use? Make dinner? Well, do you have cooking? Climb out the window? Well, do you have defenestration?).
I've been accused of being of being a grognard about this stuff (actually, Alex calling me "more Orthodox than the Pope" is something I wear as a badge of honour), so consider that context with what I'm about to say. I'll also preface with every campaign is a law unto itself, so, fill yer boots! In any case, I feel like a lot of fixes like this actually tend to do more to break the game than to fix any actual problem. I think that's a lot of what drove the development of 3.x; many small changes to fix things where people said, "Well, that's stupid!" The trouble was that a lot of things were how they were for gameplay reasons. The same is true here. Why can't you improve these tasks? Because of gameplay. Class niche protection. The trouble with over-specialization. The arguments for changing it often boil down to: it's not realistic. But of course, neither is the vast majority of the game, to a greater or lesser extent.
Do I think allowing PCs to take Adventuring as a Proficiency multiple times will actually "break" the game? No, not really. But I don't think it will make the balance (for lack of a better word) of the game better, either. Complaints about the uselessness of the Thief Class have been a thing for a looong time. This does not help that situation. At the very least, I would make it a Class Proficiency. Allowing the improvement from attention to detail of the Craftpriest has less long term impact, as it's once, but consider that it means a 1st Level Craftpriest has the same chances to Hear Noise as a 4th Level Thief, and the same chances to Find Traps as a 7th Level Thief. Does that matter? To a Thief, the answer is probably, "Yes."