The question asks what the best choice in this situation is, not a different situation. The answer does not depend on whether any other situations exist.

That they are independent is the only reasonable assumption, everything else is going out of your way to complicate the problem.

If they are NOT independent because Monty only shows you a goat behind the door if you've picked the wrong (or right) door, this is giving the game away. You don't need to guess, you always know what to pick with 100% certainty based on Monty's algorithm.

(Also, the game show doesn't work like this. And the text doesn't mention Monty's motivations, which in standard logic puzzle formulation must mean they are irrelevant, just as the phase of the Moon is also irrelevant and you must not take it into consideration)

If Monty picks randomly instead of always a goat, and he shows a car, the game has ended and no probabilities are involved, because you don't get to switch anymore; you've lost.

If Monty opens a door and there's a goat, we're within the parameters of the problem as stated (and you should switch!).

There is a genuine human language problem here, NOT A MATH PROBLEM, which accounts for two differing but self-consistent views. It is a legitimate difference in views because human language is genuinely ambiguous.

"You pick a door, the host opens another door and reveals a goat. Should you switch?"

Does this mean you are in one particular situation where the host opened a 2nd door, with a goat? Or does it mean the host always opens a 2nd door with a goat?

If the host always opens a 2nd door, showing a goat, you should switch to the third unopened door.

If all you know, is this time you picked a door, then the host revealed a goat, you don't know what to do. Maybe this host only opens goat doors after you pick the right door, in order to trick you into switching? In that case switching would be the worst thing you could do.

A host with that strategy is a special case, but special cases where a potential general solution (always switch) doesn't work, are all you need to disprove the general solution. It cannot be a general solution if their is even one special case it doesn't work.

Most people interpret the problem to mean the host always reveals goats.

But if the language isn't clear on that, then you do have a different problem, whose solution is really impossible to optimize for without some more information on general host behavior or strategies. Without that information, all you can do is flip a coin. Or always stay, or always switch. You have no means to improve your odds whatever you do.

The problem statement does put constraints on the host, by specifying that the host opened an unselected door with a goat behind it, only to ask if the player wants to change his choice. The answer to the question of whether the player should change the choice is well defined. Other variations are irrelevant since they are different problems.

Your argument is equivalent to denying that 2 + 2 = 4 is correct because the author had the option to write something other than a 2 as an operand.