Speaking as someone who's produced alcoholic beverages and has sold them in all 50 states, and who now is a senior manager for a distributor, I'll throw in my two cents.
While it's true that many states charge a fee to register your brand so as to conduct business in that state, the overwhelming majority charge fees that are not at all cost-prohibitive for a producer. And true, for many states, their charge is a per label (product) fee...but, again, it's a fairly small fee, and not at all prohibitive to business.
And while I'm not entirely a fan of the three-tier system, the choke point - at least with regards to the question posed in this post - is NOT the distributor. The issue here is availability from the supplier.
I am the State distributor for Heaven Hill, but am not able to order every item they produce...and believe me, I beg for some of them. I also sell the Sazerac portfolio, and just last week I asked our rep if I could order a few cases of AAA. "Nope, sorry, we don't sell it in Minnesota" was his response...despite the fact that I sell AA, BATC, RHF, Hancock's, Van Winkle, etc.
It really goes back to the issue of limited production, an established market for certain products, and a desire on the part of the producer to not over-commit the distribution of a product unless (or until) a consistent, adequate supply can be guaranteed. Wholesalers are in the business of making money...which means stocking the products that the customer wants, be it 500 cases or 5. We're not going to say "no" to business...unless we can't get the goods from the producer.
Mat, I too am in the distribution business. I personally know of a large Wisconsin wholesaler who has repeatedly refused to bring in solid case purchases for individual retailers. These are not import cases that need to be brought in on containers, these are individual cases that are either in Jersey or Northern California warehouses, where bringing in a case is easy. The wholesaler's response is that they won't do the paperwork for such products. This same wholesaler sells Diageo, FWIW.
The point is, many arrogant wholesalers will say no to certain business.