I'd be very interested to know how they produce it if the formula is so tightly held. At some point people need to be purchasing the ingredients and mixing them together.
The Carthusian monks who produce Chartreuse (a collection of herbal liqueurs popular for use in cocktails) have been producing it and protecting the secret 130 ingredient recipe for over 400 years successfully. At any given time no more than three of the monks hold the entire recipe, and yet they have a company they have formed to execute most of the production without the secret being leaked.
The designated monks coordinate production and are involved in QC, as well as developing new blends for special releases, but much production is done by paid employees who do not know the complete recipe.
Presumably the recipe relies on very unique and location-specific herbs to the alps. Part of the justification for limiting supply is concern for the environment and sustainability of their production. The order also had to cease production while they were evicted.
I wouldn't be surprised if some of the key ingredients weren't wild foraged or at least very unique species.
One of the greatest use cases of security by obscurity, specially if part of the ingredients are decoys.
A few years ago I (not a specialist!) made lots of batches of OpenCola, which is based partly on the original Pemberton recipe, and it comes so close that nobody could realistically tell the difference. If anything, it tastes better, because I imagine Coke doesn't use fresh, expensive essential oils (like neroli) for everything.
The tricky piece that nobody else can do is the caffeine (edit: de-cocainized coca leaf extract) derived from coca leaves. Only Coke has the license to do this, and from what I gather, a tiny, tiny bit of the flavour does come from that.
Coca leaves contain various alkaloids, but not caffeine. Coca Cola gets its caffeine from (traditionally) kola nuts, and (today, presumedly) the usual industrial sources.
I've not participated in Cola tasting, but assuming fresher tastes better isn't really a safe assumption. Lots of ingredients taste better or are better suited for recipies when they're aged. I've got pet chickens and their eggs are great, but you have to let them sit for many days if you want to hard boil them, and I'd guess baking with them may be tricky for sensitive recipies.
Anyway, even if it does taste better for whatever that means, that's not meeting the goal of tasting consistently the same as Coke, in whichever form. If you can't tell me if it's supposed to taste like Coke from a can, glass bottle, plastic bottle, or fountain, then you've told me all I need to know about how close you've replicated it.
And by fresh I do mean: The OpenCola is full of natural essential oils (orange, neroli, cinnamon, lime, lavender, lemon, nutmeg), and real natural flavor oils have a certain potent freshness you don't get in a mass-produced product.
But you are trying to reproduce a mass-produced product.
I did my OpenCola experiment in the company office together with a colleague, and we ended up hooking it up to a beer tap, with a canister of CO2. I'm proud to say the whole office really got into it.
You write code for a certain part/spec that could go on a number of things (missle, airplane, etc). You dont know if your code will be used in a missile or not.
He mentions that the ingredients are shipped unlabeled from different facilities who don't know what they're making.
He then goes on to reverse engineer the formula. Because science.
The mixing, again, spreading it out, have factory A mix ingredients x, y, and z, factory B mix ingredients Alpha, Beta, Gamma, and factory C mix factory A and B's mixtures.