What do you mean? In a flight simulator you have your controls controlling a plane (right body, dynamics are well known) in the sky (simple environment, dynamics are reasonably well known, even with different atmospheric conditions like wind). The output is visualized on the screens as a rendering of the scene.

In the case of robotic surgery simulator, you are using the controls to control the arm, but to interact with what? If you just want to move the arm around and maybe interact with some rigid objects sure that's easy. Would that add any training value to the surgeon? Probably not. You can get value only when the simulator includes a simulation of something the surgeon would have to face eventually - organic mass of the human body. Simulating that is hard, and I doubt anyone would invest much into it when you can train surgeons on alternative physical objects like pigs.

it would control a software arm operating on a software body, just like a flight sim controls a software plane.

It is nearly impossible to accurately simulate a “software body“.

Why? Couldn’t one model the various tissues and bones, fluids, surface tensions, resistance to cutting etc?

Yes, you can produce a model incorporating nonlinear elasticity, viscosity, plasticity, frictional contact, subfailure damage, and fracture / cutting. Repeat for each tissue involved. Some of those methods are well-developed, others are not. Damage and failure in particular is poorly developed, and simulating deformable body contacts can be tricky. Then you have to estimate parameters for all of that, validate that the model produces realistic outcomes, and get it to run in real time. You can ignore most of the complexity and make approximations, like treating everything as an isotropic linear elastic material, setting cutting resistance to a fixed value per tissue, treating the scalpel like a lightsaber, and accepting that contact will be imperfectly enforced (surfaces may interpenetrate). A crude simulation can still be good enough to be useful as a learning tool though, but it tends to work more like a video game than a true physics-based simulation. We'll still eventually get the kind of accurate simulation you're asking for, probably.

I was specifically constraining the discussion to robotic surgery. Do all these variables apply in that case?

Not sure how to interpret the question. Using a robot vs. a person doesn't change anything about the physics of how tissue responds to perturbation. You can of course simplify the simulator and correspondingly limit its use to specific learning objectives, probably novice-level. To return to the thread's starting point—we understand flight well enough to make general-purpose flight simulators, we don't understand tissue well enough to make general-purpose surgical simulators. You can still make simple interactive training tools to help someone rehearse the motions of a procedure, but I wouldn't call such a tool a simulator.

Very very many variables... For example, burnt tissue, crushed tissue, injection trauma, infected tissue plus variable anatomy.