Are nuke companies feasible?

Real life army supply chain work on the same principle.

Multiple companies produce weapons and other goods which are then offered to the army, which then chooses the best briber offer as official supplier and purchases the above mentioned goods.

Usually the request is stated in the form of a call for offer to meet a specific request.

Jet fighter, missile systems, guns, rifles, ammunition, chocolate, blankets, boots, the list is endless. Adding the nukes to it is almost trivial.

What you describe is almost the same as what happens today with the military-industrial complex. However, there is one key difference. You say the government purchases at regular intervals to create the market. One individual consumer is not a market. It does not obey many of the general rules that we expect markets to obey.

The key question is what is "the best products?" If there was a market, one would do market research to figure out what "the best" means. With one customer, the question becomes "what does the customer want?" This leads to open-market bidding on contracts rather than purchasing. The government states what they want and the suppliers bid for contracts to supply that.

The other key question would be "what is the government doing with all of these nuclear weapons?" Are they just letting them sit in warehouses until they reach their end of life, or are they being used actively and needing to be replaced? The former makes for an extremely inefficient government acquisitions program. The latter leads to there being more need for a large number of suppliers, but raises its own geopolitical questions.

This also assumes a very different approach to secrecy. In the modern world, nuclear secrets are some of the best kept secrets in the world. In theory, very few people know how to build these devices, and that knowledge is closely monitored. For the sort of innovation you describe, those secrets would need to be divested to corporations. This isn't a fundamental problem, per se, but it would absolutely shape the world in a way very differently than ours.

There's nothing unfeasible in principle about using a market mechanism for weapons production or a rocket program.

However: I see three secondary but significant and possibly show-stopping problems.

• Acquiring, storing, and especially moving nuclear materials around your country is a regulatory nightmare. Every administrative safety barrier and physical checkpoint designed to prevent industrial accidents, crime, and foreign attack; every regulation designed to force market actors to internalize their own externality costs; and every risk-averse local political leader who doesn't want dangerous materials transported dangerously through his community is going to actively work against you. You can't just get rid of these things - they are what keeps your whole country from going up in smoke twice a week. You have to keep them, and then you have to strong-arm your way through them. Strong states can do this. Strong-arming your way through systems that are necessary but sometimes counterproductive is half the purpose of having a state in the first place. The main problem here is not that your state can't hand over the power to strong-arm its own regulatory system to a set of corporations - it's that once it has done so, it will have a lot of trouble remaining a state. When corporations compete for sales, it's a market. When corporations compete for the mechanisms of state-applied force it's a revolution.

• Markets become inefficient under these circumstances. You appear to want efficient markets: "Through constant competition, nuclear power is rapidly and extensively explored." But you have secrecy requirements, regulatory capture, distance between the end-user and the purchaser, and political quid-pro-quo (Senator-Prelate Bob wants to give the contract to Weyland-Yutani because their factory creates high-paying jobs in his archdiocese). These all take away the principle that makes markets efficient in the first place: cheap, distributed information, relayed to the relevant local actors by the price mechanism. The people buying the product (acquisitions committee) aren't the ones who pay for it (taxpayers), and probably don't know how much it's going to cost or what exactly they're buying. The thing they want to buy (political benefits for themselves, welfare for their districts) isn't the product that they're ostensibly purchasing (weapons). The person using the product (low-level military officer) doesn't choose which one to buy, and neither does the person paying for it (taxpayers). The people in charge of making the product (military contractors) have an easy road to regulating their own product, especially given the first bullet point - thus letting them cut off upstart competitors at the knees by biasing regulations to protect insiders at the expense of outsiders.

• Offensive applications of nuclear weapons are the stated use case, but your country as defined doesn't seem to have any offensive ambitions: it is insular and occupies a whole continent. It isn't at war with the US or the USSR. Aside from strategic second-strike capability to make sure that it stays not at war with the US and USSR, it doesn't appear to have anything to want to use nuclear weapons on. You don't nuke your own city and countryside, you don't have borders to nuke if an enemy tries to roll tanks across them, and you don't even need to be able to win a nuclear exchange with anybody - you just have to make sure that the US and the USSR know that if they try to "liberate" you, they'll lose a city or two for the privilege.

Companies need constant revenues, to satisfy shareholders and or if they are private the owners of the company need to be made whole for their investments.

What possible thing could a company sell, that develops a way towards nuclear weapons? Enriched uranium hexa fluorid? Centrifuges?

The whole manhattan project was a tremendously expensive undertaking because it explored "all the possible ways" in parallel, but still where would you get the investments for, even if you had a buyer lined up in the end? Where would a company get the funds if it had to explore the whole enrichment labyrinth until it has a working way towards a device.

Companies go bankrupt for much smaller endavours not giving a reward. They are slimemolds that need constant food to explore a space. A state actor, can throw funds at them to survive the high mountain ridges of possible fruitless research and find a new valley of sustenance. But then- its is not really a company? Its a part of the state in all but name..

In your case, its the holy office of atomic inquisition with the patron saint of st. oppenheimer.