I disagree, here. One may be a masterful copier, taking a year to replicate a painting in a painstaking process, and yet not be able to successfully be a painter. I think there are a few cases of a middling to poor painter creating very good forgeries. And, remember, using a tool untrained just means you don't get a proficiency bonus. So, you can be an excellent forgery of paintings, but not be considered a 'painter'.
I've never heard of a single case of that, and I'd argue that making your own unique painting requires creativity, not skill in painting. Meanwhile, copying the flow of another person's work, their line depth, ect, requires you to understand those details and how to recreate them. Which by default, falls under the skill of the painter's tools.
Also, taking a year to copy would be the equivalent in DnD terms of taking a 20. Anyone could successfully forge something if you let them take a 20 on the skill, even if they have no skill in the relevant work.
Amusingly, since it would require a lot of money and more than 250 days, it would also potentially qualify them for proficiency in the tool set.
There's more to it than this. You're simplifying to create an equivalency that doesn't really exist. It's not a matter of buying the right supplies -- if it were that easy, then forgeries would be easy. It's a matter of knowing what you actually need to make a forgery or, how to use supplies to create a false effect than appears to be a true one. Painting weather in a few decades. It's not just a matter of getting the right paint.
But, we're in the weeds, here, arguing details. The point is, undetected forgeries cost, and people take extra care to protect against forgeries. It's not a matter of getting close in style -- if it were that easy, there's never be surety of authenticity. So, there must be something to forging things (documents, paintings, etc.) that's going above and beyond to foil the detection methods in place. We don't need to know what those details are because we can just leverage the forgery kit proficiency to tell us if a PC does a good enough job on those details to pass off a fake.
A few things.
1) I'm not caring about the countermeasures and I see that as being a red herring. Yes, forging a document can cost someone millions of gold or thousands of lives. That is why creating a forgery is difficult. But, any possible measure has two possible things in game. A) It is something that as a painter or scribe they would know about. If every real military document misspells the the word Army to show it is real, then a scribe who ever had to work on a military document would know this. Or B) Every official document needs to be sealed with a magical wax seal that is kept in the desk of the Master Scribe in the capital. In which case, you need to use it without getting caught, because you can't just replicate it.
Unless we are going to say that Forgery kits give everyone a) magic or b) the ability to make and replicate any design AND you can't do that with any other skill.
And things like again, things like aging paint or aging paper are things that people with those tools would know how to do. I have a friend who is an amateur woodworker. He knows how to quickly age wood, because he wants to make tables and desks that look antique without waiting a few decades for it to happen naturally. I could probably call up a Professor of the visual arts at a college, and ask them how to age paint to look older, and they can likely tell me.
Which is what leads into this
This is a squirrel argument. That water vehicles can be pointed at as applying to a broad category of water vehicles may or may not be a compelling argument, but it doesn't have much to do with forgery kits.
The point isn't to look at forgery kits, it is to look at Painter's Tools, of Blacksmithing tools, of Calligrapher's Supplies.
If Water Vehicles proficiency covers any floating boat shaped object, and dozens of sailing techniques, then why can't painter's tools cover knowing how to age paint? Why can't a blacksmith put a design on a rod of iron that matches the seal made of gold? Why can a jeweler not create a ring engraved with a message that looks like identical to one created by another jeweler a decade ago?
Why does it take a different proficiency to do the same thing that someone else did with the original tool?
Should it be a high Dc? Yes
Should it require special materials? Yes
Should it be difficult? Yes
Should it require an entirely different proficiency that has nothing to do with the tool that makes the object you are copying? No, why should it?
Personally, I like having a distinction between the kits if only because something called a "forgery kit" just sounds illicit. It's considered contraband, and those in possession of one are considered criminals-- just like thieves' tools.
It's not RAW, but I like to think a forgery kit contains a few high-end and ordinary doc supplies (paper, quills, ink, sealing wax, erasers, tracing paper, etc), as well as a selection of forms, letterhead, stamps, ID blanks, foil seals, unused ticket books, blank bank note, etc, swiped from official sources. It might even include some sort of fantastical configurable embossing tool, paper-aging solutions, jewelers' loup, and so forth. In addition to the basic writing &/or art skills needed, the proficiency mostly implies maintaining a working local knowledge of the jargon, codes, forms, etc, of the trades & offices being mimicked; as well as keeping the kit stocked with whatever basic docs might come in handy wherever the forger is at the time (and surreptitiously disposing of the unused illegal materials). Of course, this could mean a "forgery kit" is just "calligraphy supplies + illegal docs".
The bolded is the part I'm saying.
Sure, have a separate set of items, but the skills, the knowledge, the jargon? That makes sense to combine with the proper skill, or it is specialized knowledge that you just wouldn't know.
For example, I would never allow someone with a forgery kit to make a perfect fake die for embossing coins (not that it would actually matter in DnD). Because those dies are a heavily guarded state secrets. Without the proper background, you just don't know that.
If they wanted to, say, use their blacksmith tools and try and copy a coin that they have, I might let them make the attempt. They know metal, they know how to form metal, but it still will likely not be a perfect copy, because that requires them to get the die, and copy that. And since it is made of metal, a blacksmith can do that, but a forgery kit with paper and ink is useless for that.