Starbucks isn't about the coffee
There are countless coffee shops all over the place. In the United States, coffeeshops are so common that a town of 50,000 people will easily have a dozen of them, not counting restaurants and stands and trucks and other places that sell prepared coffee.
While most of what Starbucks sells is prepared coffee, that's not why customers choose them over other places that sell prepared coffee (to the point that a lot of longtime independent coffeeshops have gone out of business). Their coffee is better than some places but nothing special.
People in our modern world (especially in the US) value consistency. They want to know they can walk in and always get the same cup of coffee, made just how they like it. This has only gotten worse as coffeemaking (both in making the actual coffee and in pulling together the customers specific cup) is now so complex that people who go into a shop and just ask for "a cup of coffee" are ridiculed on internet joke sites. If you learn the Starbucks system, you can go anywhere in the country (and to some degree the world) and order a complex (they're all complex now) cup of coffee just how you like it and know exactly what you're getting. And guess what, people who use one shop's terminology at a different shop get ridiculed on the internet too. And in person.
Starbucks also has consistency in their cold drinks, non-coffee drinks, and their food offerings (though some locations may have larger or smaller selections). Their cups are branded (no matter the season, you'll be able to recognize a Starbucks cup). You know about what you're going to pay for stuff.
Coffeeshops are also destinations. If you want a place to sit and read or work on your laptop or chat with friends, you will have to try out a lot of coffeeshops to figure out which ones let you do what and for how long and with what access to electrical outlets. While an individual Starbucks might have somewhat different seating arrangements, and different crowds, from another, your overall experience is about the same.
When you set up a franchise, it's consistency you're selling.
Take McDonald's. This hamburger stand opened its first franchise in 1955. As their stores expanded, they did not at first ship food from central locations like they do now. Stores sourced their ingredients locally. The consistent feel came from the physical store, the menu, and the cooking style (with specific recipes, amounts, etc).
By 1981 the food coming in was shipped and ready to go and each store had to comply with the main office's specific rules.
At least the menu was blessedly simple, with about a third of today’s
100-plus items. “Back then, you could crank out a lot of burgers with
10-to-1 meat,” Jarvis says, referring to boxes of 10 burger patties
per pound. He quarterbacked his staff from the fry station near the
center of the store, becoming a stickler for following McDonald’s
exacting standards for preparing food. “French fries were our bread
and butter,” he says. “I wanted a fry person who, when the fries were
seven minutes old in the fry basket, they would throw them away. It’s
in the manual.”
Now things are so complex that going back to local sourcing is a problem. But before the national highway system, before giant trucks with freezers (even more so than giant train cars with freezers), perishable ingredients had to be local.
Keeping a franchise recognizable as such required building shops that looked alike, manuals for operation that made sure staff in one location was interchangeable with another, identical equipment, and plenty of branding. This means lots of visits from corporate to make sure a location was on track. While coffee beans transport pretty well, there's a lot more to a franchise.
You're not selling coffee beans.
You're selling coffee seeds. You're selling seeds that can be grown anywhere in the kingdom. Each agricultural operation has to be different. No matter how adapted these magic coffee plants are, each area has its own way of growing, its own sources of water and fertilizer, its own way of doing things. You aren't managing all that, nor should you. The growing would fail if you did.
Maybe you do sell the processed beans.
But say you don't sell the seeds, you only lease out the farms and allow others to grow them for you. Then you process and distribute the coffee beans which are ready to be ground up and made into coffee. That alone is a big deal and you will have different products from different regions.
So on to the franchise. The concept of a franchise only works if people go to more than one location. Otherwise, how do they know it's the same? In our modern world, we all know that a Starbucks or McDonald's is the same everywhere, even if we've been to just one of each (or zero). In your world, at least some people would need to experience it.
Not enough people travel in your kingdom. And none of them are going to care about the consistent experience. Sure, they might all want "Summerfall Coffee" (just like they all want Dornish Wine with dinner) but that's a produced product that goes through distribution channels and is available for individual inns and cafes and other places that serve food (like castles) to buy wholesale.
Would it be possible?
Possibility isn't just about the tech, like you imply. It's also cultural. Culturally, no way. There's no reason for it and no desire.
As for the tech...
- First what you need is a central office (that's more or less done).
- Well-trained enforcers (easy enough).
- You need a manual for setup and operations. That's a bit harder because everything has to be handwritten and copied and not many people know how to read.
- Franchise owners need to come to Summerfall (or other central location) for training. This is not impossible...the owners would all be 3rd and 4th sons of lesser nobles. The ones who don't want to just be knights or live in their older brother's shadow all the time. If you really want more applicants, open it up to the daughters.
- Getting into this is very very expensive.
- Once trained, the franchise owner goes back home and oversees construction, probably with an enforcer around for that.
- The owner has bought the branded company equipment and hauled it back.
- The staff doesn't have to know how to read (well the supervisors should) and their training is very specific.
- We'll allow each establishment to supply their own mugs for serving the coffee.
- Every few months, a new supply of coffee beans comes in, along with an enforcer to make sure the franchise is doing what it needs to be doing. And of course to collect their share of revenues and payment for the coffee.
With a non-perishable single product, could you handle the logistics of a franchise in that world? Yes.
Would it work out financially for all concerned? Probably not.
Would all the trouble to create a consistent experience for the customer be worth it? No.
Your customers will buy because nobody else has coffee, at least not in the north and central parts of the kingdom. You have no competition, so why does the experience matter?
You'd be better off selling the seeds or the processed beans.