I wouldn't consider the big three really all that stable. I've seen way too many dealerships, of major US makes, close their doors over the last 20 years. CNH has really had a lot of dealer movement as they have gone through their mergers with Case and International, Ford to New Holland and finally to CNH.
While there may be dealers somewhere, and not necessarily near you, willing to service you tractor there is certainly no guarantee who will be where in a decade.
In many instances dealers aren't in any hurry to service stuff they didn't sell, and if it is not under warranty the dealers have no incentive to do the repairs.
As the guy mentions above, he can't even get a simple stabilizer chain turnbuckle for his Kubota. That says it all about the "great" dealer network. A great dealer network doesn't mean squat if the dealer isn't willing to make it work for the customers.
Someone else scoffed about having to order parts. There isn't a dealership in the country that is going to have every part necessary for every model of tractor that is and has been made by a brand.
Warranties are generally three years in duration. IMO, focus on the dealer should be within that three-year period. Offering to come out and repair the tractor on site, or to trailer the tractor back to the shop for warranty work is a big deal. After the warranty period is over the big thing is parts availability. In this age of the internet this is not really the factor it once was. There probably isn't a primary or secondary brand one cannot come here to TBN and find someone willing to provide the needed parts.
The Mahindra dealer I spoke with has sold the brand since the 90's. His family has been in business selling first MF and now MF and Mahindra tractors for decades. When it comes to service I would have a lot more confidence in his dealership than some of the Kubota, CNH and John Deere dealers who are a lot less established in the area.
The dealer closest to me has sold Long tractors (now badged as Farmtrac) for three decades. They used to sell IH tractors then Case-IH tractors, but lost the dealership when the CNH merger took place. They have now picked up McCormicks to sell with the Farmtracs. The McCormick tractors came into existence as a result of the CNH merger. Like Mahindra they are an offshoot from the old IH company, and can trace those roots back to Cyrus McCormick.
Currently brands like NH, JD, MF and Kubota are not expanding their dealership networks. On the other hand Mahindra, Kioti, Branson/Century, McCormick, etc., are expanding their dealer networks. While some of these dealers are new dealerships that are springing up a number of these dealers added to these networks are dealers which have sold other brands and are now adding to their lineups, or have lost a dealership due to mergers and picked up the new brand to offset their losses.