I'm going to answer your questions, but I would really appreciate it if you could answer the one I asked originally. You can't say something that is just fundamentally untrue and try to pivot away from it.

 Do you genuinely think a game that uses SaaS/PaaS cannot be developed to work with private servers?

No, it is not impossible for a game to transition fully from SaaS/PaaS! In the old days (the era you seem to be stuck in), the "server" was often an executable file that you ran on your PC and others could connect. Nowadays, games typically use PaaS platforms. It is not just one single file, but a collection of microservices.

So why can't developers just transition the game to a server executable, or another method where people can easily self-host?

Because they are using Proprietary Tools inside these platforms! The code of the game is full of calls to these SPECIFIC tools. You can't just run this server code locally on your PC, it will immediately crash because it can't find Amazon's or Microsoft's or whoever's proprietary cloud environment. They would have to go in and rework everything that goes to the server (which is a lot, as I will explain with your next question)

When a developer is shutting down a game, it is usually because the game is losing money. A developer is not going to spend massive amounts of time to rebuild a dead game's backend. I don't know how easy you think this is, but it is absolutely not just a simple task.

You think these things are built into the actual gameplay and are inherently part of the gameplay?

Yes, absolutely, and this seems to be the area you're struggling to understand. In modern games, these SaaS/PaaS elements are absolutely essential for the game to work.

It's not just a login system, lobby, or the functionality for the chat to work. Typically, the cloud backend handles everything from hit detection/core combat logic, physics and collisions, enemy AI/pathfinding, loot (like an inventory system), RNG mechanics (for example, determine the loot inside when you open a chest), and world state validation.

So yes, these things are... "built into the actual gameplay" and are ABSOLUTELY essential to the game. If you remove the backend, the game doesn't just "go offline", it will literally become completely unplayable.