The thing is, you can't pick a lock with your bare hands, so that is why it is not a skill. Its an odd distinction, but that is how 5e does it. Like riding a horse, you can't do it without a horse, therefore it is a tool proficiency, not a skill. The lines get blurry with things skills like Medicine, as that makes you a GP, but Proficiency Healers Kit makes you a trauma surgeon. Same goes with Animal Handling not being about Riding which is Proficiency Land Animals or something similar (I let animal handling apply, as it is not an exciting skill in its own right).
There are some instances where the DM might apply disadvantage or not even allow a roll without a good reason why your untrained character could do it. For instance, most arcana checks, complex navigation calculations, knowledge of a land you have no reasonably been to or studied etc. Personally, lock picking is one of those things for me, most people can't pick up lockpick tools and have a decent chance of knowing what to do with them. They might get lucky, but I'm likely giving them disadvantage at best. The same goes for surgery and many other applications.