I'm a huge fan of overlapping skills. It speeds up the game because you don't have to think as hard about which skill is most appropriate;.
Heh heh... whereas I'm the opposite. I don't use overlapping skills because I use the optional rules of not assigning skills to abilities. So for me, it's blatantly easy to determine which of the six ability scores a check would apply to, and then after that, strongly demarcated skills makes it simple to decide which one can be added.
And that's exactly why I use the animate/inanimate Perception/Investigation split. Because for me... passive or incidental checks to sense things is a Wisdom check... an active decision on the part of the player to find things in an Intelligence check. After that's decided... it's dead simple to add in (Perception) when the hidden thing is a person or monster, or (Investigation) when it's a trap or secret door.
I can understand the major questions/concerns of seeing things versus deducing clues or actively searching for someone versus just sensing they are there... when a DM always uses Wisdom (Perception) and Intelligence (Investigation). Because the DM has to actually go into the scenario and try to determine whether the stuff to be found are purely "Hey there it is!" or more of a deduction based on spotted information and how much of that info was perceived passively and how much was concluded, and whether it should apply to the more passive Wisdom versus the more active Intelligence etc. etc.
And that's why I skip it all and not even bother trying to make those choices. For me... choose the passive ability Wisdom for the check, or the active ability Intelligence for the check. Then, for those who are proficient, add in Perception if the hidden thing is a person that moved around to get into their hidden state, or Investigation if the hidden thing doesn't move at all and was camouflaged by someone else who had to stand outside of it and stare at it and figure out the best way to hide it.
For me it makes things so much easier.