It's absurd for one character to carry around all the equipment and toolkits for every job ever in a bag of holding or in whatever and then whip it out at the appropriate moment and say "of course I'm trained in extreme pogosticking! I have an extreme pogostick, don't I?". That's the silly part.
It must be difficult to run a game where your fighter character, since he is the master of all weapons (save the asian and silly ones) popping out a new weapon every combat and declaring he is the master of all weapons. Obviously we need to return to 2e, where he was limited to a few weapon proficiencies. I mean, he knows far more styles of fighting than anyone would ever know in real life.
You must have also read that it is a common problem for the playtests of 5e that people are buying up every item they can, and cackling about how they know all the skills because it is all done with ability checks.
Also, when you play 3rd edition, whenever someone makes a planar lore check, it means that he knows the entire infinite universe, with infinite planes of existence. Within each of those infinite planes he knows something the creatures, the geography, the politics, and all the other mundane things of every single one. He isn't a learned sage, he is an infinite store of knowledge which no man could ever learn in 100 lifetimes.
Oh wait, none of those things are true, because people can handle abstraction. The scenerio you are describing is just as ludicrous as those three scenerios are.
your equipment is irrelevant in such a scenario. I said that being especially good at some aspect of play that arises should probably require some kind of resource for your character.
Then you make a charisma check without equipment. In fact, that brings up an interesting point. If you have a piece of wire or a slender dagger, and you have an ability score check system according to you, I am already a master of picking locks. I don't even need the lockpicks. That means everyone who owns a dagger in D&D next is a master locksmith. We gotta tell WotC about this right away. They're making a huge mistake!
You said that it's a sucker's choice because combat is what keeps you alive and thus if you didn't choose combat benefits you were making a mistake.
A situation where a skill might be needed to save your life comes along once and a blue moon. Monsters try to murder you every session, multiple times. Yes, it is a sucker's game spending combat feats for skill bonuses.
A character's skill lies within themselves, not with their equipment. To shift that bonus away from the player is to increase reliance on equipment and to effectively allow people to "buy" skill ranks.
So is buying a horse. You are buying skill ranks in run by using a horse. In fact, you are buying so many skills ranks, that you can run farther and faster than the fittest man. Is that a problem? A guy with a grappling hook and rope will be able to climb a wall much easier than a guy who is crawling up unaided. That's buying skill ranks too, is that a problem?
No, because of course things are easier if you buy the right tools. If you aren't expressing it as a skill bonus, how are you expressing it?
Putting it on the background on the other hand, on the player, means that you are good at something even if it doesn't make sense. Why is a merchant who gets his diplomacy check bonus for selling wares, better at negotiating with orc chieftains, winged elves, and monks who have taken vows of poverty?
Is the assumption that alchemist kits do not exist anymore? You don't need a full lab to have the necessary tools and justify "training when we weren't looking so I'm just as good as the guy who explicitly made a big deal about his training".
Oh yeah, alchemy kits. God I hate them. You cannot make glowsticks, sonic grenades and other alchemical items with a case you carry on your backpack. That's sillier than anything we're talking about.
Okay, so you don't have to buy an expensive lab with *spit* alchemy kits. But you are still only getting a slight discount on alchemical items. Not a huge difference unless alchemical items are better than your attacks or other abilities. If they are, then they shouldn't be available for mere skill points anyway. You don't get access to the complete spell list of a wizard with Knowledge: arcana, so why would you get something equal to a wizard's spell list with an alchemy skill?
Skills systems exist to establish degrees of proficiency/mastery in a variety of subjects that relate to commonly encountered scenarios while adventuring. To suggest that it's artificial is silly - this is an abstracted game we're talking about, of course it's artificial, just like almost any game mechanic. A skill system is not there to say "no", it's there to provide a resolution system for scenarios.
The degrees of proficiency can be established just fine with ability scores, you don't need a skill system for that. Having both is just redundant. Especially, since if you want to be effective, you pretty much have to max out the skills the best you can all the time. That's why 4e did away with skill points, because it was a waste of time to have less than the full amount.
Skyrim went the other way and ditched stats and kept skills. It however, just lets you do what you want to do and does the book keeping for you, adding skill ranks as you go along. I would like 3e's skill system a lot better if I got a skill rank every time I used a skill. At least I wouldn't be hemmed in at an arbitrarily low level of general competence.
I don't know why you don't think skill points can be allocated in a way that makes sense, as that runs counter to my experiences.
I told you, because there is never enough skill points to represent an adventurer doing things that an adventurer should do.
This is why I don't ask for skill checks unless they're trying to accomplish something more difficult than cooking a meal. I also allow people to try anything (trained or otherwise), and give plenty of skill points and other options to increase proficiency.
If you want people to do a wide variety of things, why not just let them do a wide variety of things? Why waste everybody's time with all this piddly book-keeping? We both end up in the same place, PC's that can do some things better than others. I just save paper and time.
A skill system is not generally there to describe every single life skill you've ever picked up, but rather it's there to describe which common actions you're good at, and you can scribble in the few uncommon skills you're exceptional at. Otherwise, assume it's a flat ability check. That should work fine.
But you already know what tasks you are good and exceptional at when you make a flat ability check. You are exceptional at tasks related to your exceptional scores, mediocre at those related to your mediocre scores, and poor at those related to your poor scores.
Why bother with a skill system except to say that you are worse at even more stuff that because you didn't invest the skill ranks?
In a system without a formal skill subsystem, I'd much rather have a player tell me "I'm a locksmith" than them say "I have some picks, so I'm a locksmith". It's just backwards and unnecessary.
Don't worry, a player wouldn't tell you that. He might say "I'm picking some locks on my equipment list so I can be a locksmith", but that is exactly like a 3e fighter saying "I'm choosing to own a sword so I can be a swordsman." He could have just as easily said "I'm going to be own a spear so I can be a spearman".
My system is exactly the same as that, only applying to more than fighter weapons.